Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions

Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions

Need instant homework help or assignment help while solving the Algebra 1 Questions? Then, Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions guide is the perfect one to overcome your hurdles. Based on the common core standards, our subject experts prepared this BIM Math Algebra 1 Solution key for Chapter 4 Writing Linear Functions. You can observe step-by-step explanations for all questions covered on Ch 5 Big Ideas Math Algebra 1 Answers Pdf. With the help of BIM Algebra 1 Ch 5 Writing Linear Functions Solutions pdf, students can easily understand the concepts & learn efficiently for their examinations.

Big Ideas Math Book Algebra 1 Solutions for Chapter 4 Writing Linear Functions

Utilize the Big Ideas Math Algebra 1 Textbook Solutions for Ch 4 Writing Linear Functions concepts and practice to the next level. Students can attempt any type of questions asked from chapter 4 in the examination after practicing the questions covered in the Big Ideas Math Algebra 1 Chapter 4 Writing Linear Functions Answer Key. Access the links provided below and solve the respective exercise of Ch 4 Algebra 1 BIM Textbook Solutions. Also, you can test your knowledge of the 4th chapter writing linear functions topics by referring to this ultimate Big Ideas Math Algebra 1 Chapter 4 Writing Linear Functions Answers Guide.

Writing Linear Functions Maintaining Mathematical Proficiency

Use the graph to answer the question.

Question 1.
What ordered pair corresponds to point G?

Question 2.
What ordered pair corresponds to point D?

question 3.
Which point is located in Quadrant I?

Question 4.
Which point is located in Quadrant IV?

Solve the equation for y.

Question 5.
x – y = 5

Question 6.
6x + 3y = -1

Question 7.
0 = 2y – 8x + 10

Question 8.
-x + 4y – 28 = 0

Question 9.
2y + 1 – x = 7x

Question 10.
y – 4 = 3x + 5y

Question 11.
ABSTRACT REASONING
Both coordinates of the point (x, y) are multiplied by a negative number. How does this change the location of the point? Be sure to consider points originally located in all four quadrants.

Writing Linear Functions Mathematical Practices

Monitoring Progress

Question 1.
You work 37\(\frac{1}{2}\) hours and earn $352.50. What is your hourly wage?

Question 2.
You drive 1244.5 miles and use 47.5 gallons of gasoline. What is your car’s gas mileage (in miles per gallon)?

Question 3.
You drive 236 miles in 4.6 hours. At the same rate, how long will it take you to drive 450 miles?

Lesson 4.1 Writing Equations in Slope-Intercept Form

Essential Question

Given the graph of a linear function, how can you write an equation of the line?

EXPLORATION 1
Writing Equations in Slope-Intercept Form
Work with a partner.

  • Find the slope and y-intercept of each line.
  • Write an equation of each line in slope-intercept form.
  • Use a graphing calculator to verify your equation.

Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 1

EXPLORATION 2
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 2
Mathematical Modeling
Work with a partner. The graph shows the cost of a smartphone plan.
a. What is the y-intercept of the line? Interpret the y-intercept in the context of the problem.
b. Approximate the slope of the line. Interpret the slope in the context of the problem.
c. Write an equation that represents the cost as a function of data usage.
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 3

Communicate Your Answer

Question 3.
Given the graph of a linear function, how can you write an equation of the line?

Question 4.
Give an example of a graph of a linear function that is different from those above. Then use the graph to write an equation of the line.

4.1 Lesson

Monitoring Progress

Write an equation of the line with the given slope and y-intercept.

Question 1.
slope = 7; y-intercept = 2

Question 2.
slope = \(\frac{1}{3}\) ; y-intercept = -1

Write an equation of the line in slope-intercept form.

Question 3.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 4

Question 4.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 5

Question 5.
Write an equation of the line that passes through (0, -2) and (4, 10).

Question 6.
Write a linear function g with the values g(0) = 9 and g(8) = 7.

Monitoring Progress

Question 7.
The corresponding data for electricity generated by hydropower are 248 million megawatt hours in 2007 and 277 million megawatt hours in 2012. Write a linear model that represents the number of megawatt hours generated by hydropower as a function of the number of years since 2007.

Writing Equations in Slope-Intercept Form 4.1 Exercises

Question 1.
COMPLETE THE SENTENCE
A linear function that models a real-life situation is called a __________.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 1

Question 2.
WRITING
Explain how you can use slope-intercept form to write an equation of a line given its slope and y-intercept.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3–8, write an equation of the line with the given slope and y-intercept.

Question 3.
slope: 2
y-intercept: 9
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 3

Question 4.
slope: 0
y-intercept: 5
Answer:

Question 5.
slope: -3
y-intercept: 0
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 5

Question 6.
slope: -7
y-intercept: 1
Answer:

Question 7.
slope: \(\frac{2}{3}\)
y-intercept: -8
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 7

Question 8.
slope: –\(\frac{3}{4}\)
y-intercept: -6
Answer:

In Exercises 9–12, write an equation of the line in slope-intercept form.

Question 9.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 6
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 9

Question 10.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 7
Answer:

Question 11.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 8
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 11

Question 12.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 9
Answer:

In Exercises 13–18, write an equation of the line that passes through the given points.

Question 13.
(3, 1), (0, 10)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 13

Question 14.
(2, 7), (0, -5)
Answer:

Question 15.
(2, -4), (0, -4)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 15

Question 16.
(-6, 0), (0, -24)
Answer:

Question 17.
(0, 5), (-1.5, 1)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 17

Question 18.
(0, 3), (-5, 2.5)
Answer:

In Exercises 19–24, write a linear function f with the given values.

Question 19.
f(0) = 2, f(2) = 4
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 19

Question 20.
f(0) = 7, f(3) = 1
Answer:

Question 21.
f(4) = -3, f(0) = -2
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 21

Question 22.
f(5) = -1, f(0) = -5
Answer:

Question 23.
f(-2) = 6, f(0) = -4
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 23

Question 24.
f(0) = 3, f(-6) = 3
Answer:

In Exercises 25 and 26, write a linear function f with the given values.

Question 25.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 10
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 25

Question 26.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 11
Answer:

Question 27.
ERROR ANALYSIS
Describe and correct the error in writing an equation of the line with a slope of 2 and a y-intercept of 7.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 12
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 27

Question 28.
ERROR ANALYSIS
Describe and correct the error in writing an equation of the line shown.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 13
Answer:

Question 29.
MODELING WITH MATHEMATICS
In 1960, the world record for the men’s mile was 3.91 minutes. In 1980, the record time was 3.81 minutes.
a. Write a linear model that represents the world record (in minutes) for the men’s mile as a function of the number of years since 1960.
b. Use the model to estimate the record time in 2000 and predict the record time in 2020.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 29

Question 30.
MODELING WITH MATHEMATICS
A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $75 per hour.
a. Write a linear model that represents the total cost of recording an album as a function of studio time (in hours).
b. Is it less expensive to purchase 12 hours of recording time at the studio or a $750 music software program that you can use to record on your own computer? Explain.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 14
Answer:

Question 31.
WRITING
A line passes through the points (0, -2) and (0, 5). Is it possible to write an equation of the line in slope-intercept form? Justify your answer.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 31

Question 32.
THOUGHT PROVOKING
Describe a real-life situation involving a linear function whose graph passes through the points.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 15
Answer:

Question 33.
REASONING
Recall that the standard form of a linear equation is Ax + By = C. Rewrite this equation in slope-intercept form. Use your answer to find the slope and y-intercept of the graph of the equation -6x + 5y = 9.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 33

Question 34.
MAKING AN ARGUMENT
Your friend claims that given f(0) and any other value of a linear function f, you can write an equation in slope-intercept form that represents the function. Your cousin disagrees, claiming that the two points could lie on a vertical line. Who is correct? Explain.
Answer:

Question 35.
ANALYZING A GRAPH
Line ℓ is a reflection in the x-axis of line k. Write an equation that represents line k.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 16
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 35

Question 36.
HOW DO YOU SEE IT?
The graph shows the approximate U.S. box office revenues (in billions of dollars) from 2000 to 2012, where x = 0 represents the year 2000.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 17
a. Estimate the slope and y-intercept of the graph.
b. Interpret your answers in part (a) in the context of the problem.
c. How can you use your answers in part (a) to predict the U.S. box office revenue in 2018?
Answer:

Question 37.
ABSTRACT REASONING
Show that the equation of the line that passes through the points (0, b) and (1, b + m) is y = mx + b. Explain how you can be sure that the point (-1, b – m) also lies on the line.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 37

Maintaining Mathematical Proficiency

Solve the equation. (Section 1.3)

Question 38.
3(x – 15) = x + 11
Answer:

Question 39.
-4y – 10 = 4(y – 3)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 39

Question 40.
2(3d + 3) = 7 + 6d
Answer:

Question 41.
-5(4 – 3n) = 10(n – 2)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 41

Use intercepts to graph the linear equation. (Section 3.4)

Question 42.
-4x + 2y = 16
Answer:

Question 43.
3x + 5y = -15
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 43

Question 44.
x – 6y = 24
Answer:

Question 45.
-7x – 2y = -21
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.1 Question 45

Lesson 4.2 Writing Equations in Point-Slope Form

Essential Question
How can you write an equation of a line when you are given the slope and a point on the line?

EXPLORATION 1
Writing Equations of Lines
Work with a partner.

  • Sketch the line that has the given slope and passes through the given point.
  • Find the y-intercept of the line.
  • Write an equation of the line.

Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 18

EXPLORATION 2
Writing a Formula
Work with a partner.

The point (x1, y1) is a given point on a nonvertical line. The point (x, y) is any other point on the line. Write an equation that represents the slope m of the line. Then rewrite this equation by multiplying each side by the difference of the x-coordinates to obtain the point-slope form of a linear equation.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 19

EXPLORATION 3
Writing an Equation
Work with a partner.

For four months, you have saved $25 per month. You now have $175 in your savings account.
a. Use your result from Exploration 2 to write an equation that represents the balance A after t months.
b. Use a graphing calculator to verify your equation.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 20
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 21

Communicate Your Answer

Question 4.
How can you write an equation of a line when you are given the slope and a point on the line?

Question 5.
Give an example of how to write an equation of a line when you are given the slope and a point on the line. Your example should be different from those above.

4.2 Lesson

Monitoring Progress

Write an equation in point-slope form of the line that passes through the given point and has the given slope.

Question 1.
(3, -1); m = -2

Question 2.
(4, 0); m = – \(\frac{2}{3}\)

Write an equation in slope-intercept form of the line that passes through the given points.

Question 3.
(1, 4), (3, 10)

Question 4.
(-4, -1), (8, -4)

Question 5.
Write a linear function g with the values g(2) = 3 and g(6) = 5.

Question 6.
You pay an installation fee and a monthly fee for Internet service. The table shows the total cost for different numbers of months. Can the situation be modeled by a linear equation? Explain. If possible, write a linear model that represents the total cost as a function of the number of months.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 22

Writing Equations in Point-Slope Form 4.2 Exercises

Vocabulary and Core Concept Check

Question 1.
USING STRUCTURE
Without simplifying, identify the slope of the line given by the equation y – 5 = -2(x + 5). Then identify one point on the line.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 1

Question 2.
WRITING
Explain how you can use the slope formula to write an equation of the line that passes through (3, -2) and has a slope of 4.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3−10, write an equation in point-slope form of the line that passes through the given point and has the given slope.

Question 3.
(2, 1); m = 2
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 3

Question 4.
(3, 5); m = -1
Answer:

Question 5.
(7, -4); m = -6
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 5

Question 6.
(-8, -2); m = 5
Answer:

Question 7.
(9, 0); m = -3
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 7

Question 8.
(0, 2); m = 4
Answer:

Question 9.
(-6, 6); m – \(\frac{3}{2}\)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 9

Question 10.
(5, -12); m = –\(\frac{2}{5}\)
Answer:

In Exercises 11−14, write an equation in slope-intercept form of the line shown.

Question 11.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 23
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 11

Question 12.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 24
Answer:

Question 13.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 25
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 13

Question 14.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 26
Answer:

In Exercises 15−20, write an equation in slope-intercept form of the line that passes through the given points.

Question 15.
(7, 2), (2, 12)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 15

Question 16.
(6, -2), (12, 1)
Answer:

Question 17.
(6, -1), (3, -7)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 17

Question 18.
(-2, 5), (-4, -5)
Answer:

Question 19.
(1, -9), (-3, -9)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 19

Question 20.
(-5, 19), (5, 13)
Answer:

In Exercises 21−26, write a linear function f with the given values.

Question 21.
f(2) = -2, f(1) = 1
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 21

Question 22.
f(5) = 7, f(-2) = 0
Answer:

Question 23.
f(-4) = 2, f(6) = -3
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 23

Question 24.
f(-10) = 4, f(-2) = 4
Answer:

Question 25.
f(-3) = 1, f(13) = 5
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 25

Question 26.
f(-9) = 10, f(-1) = -2
Answer:

In Exercises 27−30, tell whether the data in the table can be modeled by a linear equation. Explain. If possible, write a linear equation that represents y as a function of x.

Question 27.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 27
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 27

Question 28.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 28
Answer:

Question 29.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 29
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 29

Question 30.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 30
Answer:

Question 31.
ERROR ANALYSIS
Describe and correct the error in writing a linear function g with the values g(5) = 4 and g(3) = 10.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 31
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 31

Question 32.
ERROR ANALYSIS
Describe and correct the error in writing an equation of the line that passes through the points (1, 2) and (4, 3).
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 32
Answer:

Question 33.
MODELING WITH MATHEMATICS
You are designing a sticker to advertise your band. A company charges $225 for the first 1000 stickers and $80 for each additional 1000 stickers.
a. Write an equation that represents the total cost (in dollars) of the stickers as a function of the number (in thousands) of stickers ordered.
b. Find the total cost of 9000 stickers.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 33

Question 34.
MODELING WITH MATHEMATICS
You pay a processing fee and a daily fee to rent a beach house. The table shows the total cost of renting the beach house for different numbers of days.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 33
a. Can the situation be modeled by a linear equation? Explain.
b. What is the processing fee? the daily fee?
c. You can spend no more than $1200 on the beach house rental. What is the maximum number of days you can rent the beach house?
Answer:

Question 35.
WRITING
Describe two ways to graph the equation y – 1 = \(\frac{3}{2}\)(x – 4).
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 35.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 35.2

Question 36.
THOUGHT PROVOKING
The graph of a linear function passes through the point (12, -5) and has a slope of \(\frac{2}{5}\). Represent this function in two other ways.
Answer:

Question 37.
REASONING
You are writing an equation of the line that passes through two points that are not on the y-axis. Would you use slope-intercept form or point-slope form to write the equation? Explain.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 37

Question 38.
HOW DO YOU SEE IT? The graph shows two points that lie on the graph of a linear function.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 34
a. Does the y-intercept of the graph of the linear function appear to be positive or negative? Explain.
b. Estimate the coordinates of the two points. How can you use your estimates to confirm your answer in part (a)?
Answer:

Question 39.
CONNECTION TO TRANSFORMATIONS
Compare the graph of y = 2x to the graph of y – 1 = 2(x + 3). Make a conjecture about the graphs of y = mx and y – k = m(x – h).
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 39

Question 40.
COMPARING FUNCTIONS
Three siblings each receive money for a holiday and then spend it at a constant weekly rate. The graph describes Sibling A’s spending, the table describes Sibling B’s spending, and the equation y = -22.5x + 90 describes Sibling C’s spending. The variable y represents the amount of money left after x weeks.
Big Ideas Math Answer Key Algebra 1 Chapter 4 Writing Linear Functions 35
a. Which sibling received the most money? the least money?
b. Which sibling spends money at the fastest rate? the slowest rate?
c. Which sibling runs out of money first? last?
Answer:

Maintaining Mathematical Proficiency

Write the reciprocal of the number.

Question 41.
5
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 41

Question 42.
-8
Answer:

Question 43.
–\(\frac{2}{7}\)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.2 Question 43

Question 44.
\(\frac{3}{2}\)
Answer:

Lesson 4.3 Writing Equations of Parallel and Perpendicular Lines

Essential Equation
How can you recognize lines that are parallel or perpendicular?

EXPLORATION 1
Recognizing Parallel Lines
Work with a partner.
Write each linear equation in slope-intercept form. Then use a graphing calculator to graph the three equations in the same square viewing window. (The graph of the first equation is shown.) Which two lines appear parallel? How can you tell?
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 36

EXPLORATION 2
Recognizing Perpendicular Lines
Work with a partner.
Write each linear equation in slope-intercept form. Then use a graphing calculator to graph the three equations in the same square viewing window. (The graph of the first equation is shown.) Which two lines appear perpendicular? How can you tell?
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 37

Communicate Your Answer

Question 3.
How can you recognize lines that are parallel or perpendicular?

Question 4.
Compare the slopes of the lines in Exploration 1. How can you use slope to determine whether two lines are parallel? Explain your reasoning.

Question 5.
Compare the slopes of the lines in Exploration 2. How can you use slope to determine whether two lines are perpendicular? Explain your reasoning.

4.3 Lesson

Question 1.
Line a passes through (-5, 3) and (-6, -1). Line b passes through (3, -2) and (2, -7). Are the lines parallel? Explain.

Question 2.
Write an equation of the line that passes through (-4, 2) and is parallel to the line y = \(\frac{1}{4}\)x + 1

Monitoring Progress

Question 3.
Determine which of the lines, if any, are parallel or perpendicular. Explain.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 38

Question 4.
Write an equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x – 1.

Question 5.
In Example 5, a boat is traveling parallel to the shoreline and passes through (9, 3). Write an equation that represents the path of the boat.

Writing Equations of Parallel and Perpendicular Lines 4.3 Exercises

Vocabulary and Core Concept Check

Question 1.
COMPLETE THE SENTENCE
Two distinct nonvertical lines that have the same slope are ____.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 1

Question 2.
VOCABULARY
Two lines are perpendicular. The slope of one line is –\(\frac{5}{7}\). What is the slope of the other line? Justify your answer.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3–8, determine which of the lines, if any, are parallel. Explain.

Question 3.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 39
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 3

Question 4.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 40
Answer:

Question 5.
Line a passes through (-1, -2) and (1, 0).
Line b passes through (4, 2) and (2, -2).
Line c passes through (0, 2) and (-1, 1).
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 5

Question 6.
Line a passes through (-1, 3) and (1, 9).
Line b passes through (-2, 12) and (-1, 14).
Line c passes through (3, 8) and (6, 10).
Answer:

Question 7.
Line a: 4y + x = 8
Line b: 2y + x = 4
Line c: 2y = -3x + 6
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 7.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 7.2

Question 8.
Line a: 3y – x = 6
Line b: 3y = x + 18
Line c: 3y – 2x = 9
Answer:

In Exercises 9–12, write an equation of the line that passes through the given point and is parallel to the given line.

Question 9.
(-1, 3); y = 2x + 2
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 9

Question 10.
(1, 2); y = -5x + 4
Answer:

Question 11.
(18, 2); 3y – x = -12
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 11

Question 12.
(2, -5); 2y = 3x + 10
Answer:

In Exercises 13–18, determine which of the lines, if any, are parallel or perpendicular. Explain.

Question 13.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 41
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 13

Question 14.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 42
Answer:

Question 15.
Line a passes through (-2, 1) and (0, 3).
Line b passes through (4, 1) and (6, 4).
Line c passes through (1, 3) and (4, 1).
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 15

Question 16.
Line a passes through (2, 10) and (4, 13).
Line b passes through (4, 9) and (6, 12).
Line c passes through (2, 10) and (4, 9).
Answer:

Question 17.
Line a: 4x – 3y = 2
Line b: y = \(\frac{4}{3}\)x + 2
Line c: 4y + 3x = 4
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 17

Question 18.
Line a: y = 6x – 2
Line b: 6y = -x
Line c: y + 6x = 1
Answer:

In Exercises 19–22, write an equation of the line that passes through the given point and is perpendicular to the given line.

Question 19.
(7, 10); y = \(\frac{1}{2}\)x – 9
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 19

Question 20.
(-4, -1); y = \(\frac{4}{3}\)x + 6
Answer:

Question 21.
(-3, 3); 2y = 8x – 6
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 21

Question 22.
(8, 1); 2y + 4x = 12
Answer:

In Exercises 23 and 24, write an equation of the line that passes through the given point and is (a) parallel and(b) perpendicular to the given line.

Question 23.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 43
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 23

Question 24.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 44
Answer:

Question 25.
ERROR ANALYSIS
Describe and correct the error in writing an equation of the line that passes through (1, 3) and is parallel to the line y = \(\frac{1}{4}\)x + 2.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 45
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 25

Question 26.
ERROR ANALYSIS
Describe and correct the error in writing an equation of the line that passes through (4, -5) and is perpendicular to the line y = \(\frac{1}{3}\)x + 5.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 46
Answer:

Question 27.
MODELING WITH MATHEMATICS
A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 47
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 27

Question 28.
MODELING WITH MATHEMATICS
A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area at the point (4, 5). Write an equation that represents the path.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 48
Answer:

Question 29.
MATHEMATICAL CONNECTIONS
The vertices of a quadrilateral are A(2, 2), B(6, 4), C(8, 10), and D(4, 8).
a. Is quadrilateral ABCD a parallelogram? Explain.
b. Is quadrilateral ABCD a rectangle? Explain.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 29.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 29.2

Question 30.
USING STRUCTURE
For what value of a are the graphs of 6y = -2x + 4 and 2y = ax – 5 parallel? perpendicular?
Answer:

Question 31.
MAKING AN ARGUMENT
A hockey puck leaves the blade of a hockey stick, bounces off a wall, and travels in a new direction, as shown. Your friend claims the path of the puck forms a right angle. Is your friend correct? Explain.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 49
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 31

Question 32.
HOW DO YOU SEE IT?
A softball academy charges students an initial registration fee plus a monthly fee. The graph shows the total amounts paid by two students over a 4-month period. The lines are parallel.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 50
a. Did one of the students pay a greater registration fee? Explain.
b. Did one of the students pay a greater monthly fee? Explain.
Answer:

REASONING
In Exercises 33–35, determine whether the statement is always, sometimes, or never true. Explain your reasoning.

Question 33.
Two lines with positive slopes are perpendicular.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 33

Question 34.
A vertical line is parallel to the y-axis.
Answer:

Question 35.
Two lines with the same y-intercept are perpendicular.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 35

Question 36.
THOUGHT PROVOKING
You are designing a new logo for your math club. Your teacher asks you to include at least one pair of parallel lines and at least one pair of perpendicular lines. Sketch your logo in a coordinate plane. Write the equations of the parallel and perpendicular lines.
Answer:

Maintaining Mathematical Proficiency

Determine whether the relation is a function. Explain. (Section 3.1)

Question 37.
(3, 6), (4, 8), (5, 10), (6, 10), (7, 14)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.3 Question 37

Question 38.
(-1, 6), (1, 4), (-1, 2), (1, 6), (-1, 5)
Answer:

Writing Linear Functions Study Skills: Getting Actively Involved in Class

4.1–4.3 What Did You Learn

Core Vocabulary
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 51

Core Concepts

Section 4.1
Using Slope-Intercept Form, p. 176

Section 4.2
Using Point-Slope Form, p. 182

Section 4.3
Parallel Lines and Slopes, p. 188
Perpendicular Lines and Slopes, p. 189

Mathematical Practices

Question 1.
How can you explain to yourself the meaning of the graph in Exercise 36 on page 180?

Question 2.
How did you use the structure of the equations in Exercise 39 on page 186 to make a conjecture?

Question 3.
How did you use the diagram in Exercise 31 on page 192 to determine whether your friend was correct?

Study Skills

Getting Actively Involved in Class

If you do not understand something at all and do not even know how to phrase a question, just ask for clarification. You might say something like, “Could you please explain the steps in this problem one more time?”If your teacher asks for someone to go up to the board, volunteer. The student at the board often receives additional attention and instruction to complete the problem.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 52

Writing Linear Functions 4.1 – 4.3

4.1 – 4.3 Quiz

Write an equation of the line in slope-intercept form. (Section 4.1)

Question 1.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 53

Question 2.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 54

Question 3.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 55

Write an equation in point-slope form of the line that passes through the given points. (Section 4.2)

Question 4.
(-2, 5), (1, -1)

Question 5.
(-3, -2), (2, -1)

Question 6.
(1, 0), (4, 4)

Write a linear function f with the given values. (Section 4.1 and Section 4.2)

Question 7.
f(0) = 2, f(5) = -3

Question 8.
f(-1) = -6, f(4) = -6

Question 9.
f(-3) = -2, f(-2) = 3

Determine which of the lines, if any, are parallel or perpendicular. Explain. (Section 4.3)

Question 10.
Line a passes through (-2, 2) and (2, 1).
Line b passes through (1, -8) and (3, 0).
Line c passes through (-4, -3) and (0, -2).

Question 11.
Line a: 2x + 6y = -12
Line b: y = \(\frac{3}{2}\)x – 5
Line c : 3x – 2y = -4

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line. (Section 4.3)

Question 12.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 56

Question 13.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 57

Question 14.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 58

Question 15.
A website hosting company charges an initial fee of $48 to set up a website. The company charges $44 per month to maintain the website. (Section 4.1)
a. Write a linear model that represents the total cost of setting up and maintaining a website as a function of the number of months it is maintained.
b. Find the total cost of setting up a website and maintaining it for 6 months.
c. A different website hosting company charges $62 per month to maintain a website, but there is no initial set-up fee. You have $620. At which company can you set up and maintain a website for the greatest amount of time? Explain.

Question 16.
The table shows the amount of water remaining in a water tank as it drains. Can the situation be modeled by a linear equation? Explain. If possible, write a linear model that represents the amount of water remaining in the tank as a function of time. (Section 4.2)
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 59

Lesson 4.4 Scatter Plots and Lines of Fit

Essential Question

How can you use a scatter plot and a line of fit to make conclusions about data?
A scatter plot is a graph that shows the relationship between two data sets. The two data sets are graphed as ordered pairs in a coordinate plane.

EXPLORATION 1
Finding a Line of Fit
Work with a partner.
A survey was taken of 179 married couples. Each person was asked his or her age. The scatter plot shows the results.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 60
a. Draw a line that approximates the data. Write an equation of the line. Explain the method you used.
b. What conclusions can you make from the equation you wrote? Explain your reasoning.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 61

EXPLORATION 2
Work with a partner.
The scatter plot shows the median ages of American women at their first marriage for selected years from 1960 through 2010.
a. Draw a line that approximates the data. Write an equation of the line. Explain the method you used.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 62
b. What conclusions can you make from the equation you wrote?
c. Use your equation to predict the median age of American women at their first marriage in the year 2020.

Communicate Your Answer

Question 3.
How can you use a scatter plot and a line of fit to make conclusions about data?

Question 4.
Use the Internet or some other reference to find a scatter plot of real-life data that is different from those given above. Then draw a line that approximates the data and write an equation of the line. Explain the method you used.

4.4 Lesson

Monitoring Progress

Question 1.
How many calories are in the smoothie that contains 51 grams of sugar?

Question 2.
How many grams of sugar are in the smoothie that contains 250 calories?

Make a scatter plot of the data. Tell whether the data show a positive, a negative, or no correlation.

Question 3.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 63

Question 4.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 64

Question 5.
The following data pairs show the monthly income x (in dollars) and the monthly car payment y (in dollars) of six people: (2100, 410), (1650, 315), (1950, 405), (1500, 295), (2250, 440), and (1800, 375). Write an equation that models the monthly car payment as a function of the monthly income. Interpret the slope and y-intercept of the line of fit.

Scatter Plots and Lines of Fit 4.4 Exercises

Question 1.
COMPLETE THE SENTENCE
When data show a positive correlation, the dependent variable tends to ____________ as the independent variable increases.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 1

Question 2.
VOCABULARY
What is a line of fit?
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3–6, use the scatter plot to fill in the missing coordinate of the ordered pair.

Question 3.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 65
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 3

Question 4.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 203
Answer:

Question 5.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 67
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 5

Question 6.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 69
Answer:

Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 70

Question 7.
INTERPRETING A SCATTER PLOT
The scatter plot shows the hard drive capacities (in gigabytes) and the prices (in dollars) of 10 laptops.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 71
a. What is the price of the laptop with a hard drive capacity of 8 gigabytes?
b. What is the hard drive capacity of the $1200 laptop?
c. What tends to happen to the price as the hard drive capacity increases?
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 7

Question 8.
INTERPRETING A SCATTER PLOT
The scatter plot shows the earned run averages and the winning percentages of eight pitchers on a baseball team.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 72
a. What is the winning percentage of the pitcher with an earned run average of 4.2?
b. What is the earned run average of the pitcher with a winning percentage of 0.33?
c. What tends to happen to the winning percentage as the earned run average increases?
Answer:

In Exercises 9–12, tell whether x and y show a positive, a negative, or no correlation.

Question 9.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 73
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 9

Question 10.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 74
Answer:

Question 11.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 75
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 11

Question 12.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 76
Answer:

In Exercises 13 and 14, make a scatter plot of the data. Tell whether x and y show a positive, a negative, or no correlation.

Question 13.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 77
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 13

Question 14.
Big Ideas Math Algebra 1 Solutions Chapter 4 Writing Linear Functions 78
Answer:

Question 15.
MODELING WITH MATHEMATICS
The table shows the world birth rates y (number of births per 1000 people) x years since 1960.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 79
a. Write an equation that models the birthrate as a function of the number of years since 1960.
b. Interpret the slope and y-intercept of the line of fit.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 15.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 15.2

Question 16.
MODELING WITH MATHEMATICS
The table shows the total earnings y (in dollars) of a food server who works x hours.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 80
a. Write an equation that models the server’s earnings as a function of the number of hours the server works.
b. Interpret the slope and y-intercept of the line of fit.
Answer:

Question 17.
OPEN-ENDED
Give an example of a real-life data set that shows a negative correlation.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 17

Question 18.
MAKING AN ARGUMENT
Your friend says that the data in the table show a negative correlation because the dependent variable y is decreasing. Is your friend correct? Explain.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 81
Answer:

Question 19.
USING TOOLS
Use a ruler or a yardstick to find the heights and arm spans of five people.
a. Make a scatter plot using the data you collected. Then draw a line of fit for the data.
b. Interpret the slope and y-intercept of the line of fit.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 19.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 19.2

Question 20.
THOUGHT PROVOKING
A line of fit for a scatter plot is given by the equation y = 5x + 20. Describe a real-life data set that could be represented by the scatter plot.
Answer:

Question 21.
WRITING
When is data best displayed in a scatter plot, rather than another type of display, such as a bar graph or circle graph?
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 21

Question 22.
HOW DO YOU SEE IT?
The scatter plot shows part of a data set and a line of fit for the data set. Four data points are missing. Choose possible coordinates for these data points.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 82
Answer:

Question 23.
REASONING
A data set has no correlation. Is it possible to find a line of fit for the data? Explain.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 23

Question 24.
ANALYZING RELATIONSHIPS
Make a scatter plot of the data in the tables. Describe the relationship between the variables. Is it possible to fit a line to the data? If so, write an equation of the line. If not, explain why.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 83
Answer:

Maintaining Mathematical Proficiency

Evaluate the function when x = −3, 0, and 4. (Section 3.3)

Question 25.
g(x) = 6x
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 25

Question 26.
h(x) = -10x
Answer:

Question 27.
f(x) = 5x – 8
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.4 Question 27

Question 28.
v(x) = 14 – 3x
Answer:

Lesson 4.5 Analyzing Lines of Fit

Essential Question
How can you analytically find a line of best fit for a scatter plot?

EXPLORATION 1
Finding a Line of Best Fit
Work with a partner.

The scatter plot shows the median ages of American women at their first marriage for selected years from 1960 through 2010. In Exploration 2 in Section 4.4, you approximated a line of fit graphically. To find the line of best fit, you can use a computer, spreadsheet, or graphing calculator that has a linear regression feature.
a. The data from the scatter plot is shown in the table. Note that 0, 5, 10, and so on represent the numbers of years since 1960. What does the ordered pair (25, 23.3) represent?
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 84
b. Use the linear regression feature to find an equation of the line of best fit. You should obtain results such as those shown below.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 85
c. Write an equation of the line of best fit. Compare your result with the equation you obtained in Exploration 2 in Section 4.4.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 85.1

Communicate Your Answer

Question 2.
How can you analytically find a line of best fit for a scatter plot?

Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 86
Question 3.
The data set relates the number of chirps per second for striped ground crickets and the outside temperature in degrees Fahrenheit. Make a scatter plot of the data. Then find an equation of the line of best fit. Use your result to estimate the outside temperature when there are 19 chirps per second.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 87

4.5 Lesson

Monitoring Progress

Question 1.
The table shows the attendances y (in thousands) at an amusement park from 2005 to 2014, where x = 0 represents the year 2005. The equation y = -9.8x + 850 models the data. Is the model a good fit?
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 88

Question 2.
Use the data in Monitoring Progress Question 1.
(a) Use a graphing calculator to find an equation of the line of best fit. Then plot the data and graph the equation in the same viewing window.
(b) Identify and interpret the correlation coefficient.
(c) Interpret the slope and y-intercept of the line of best fit.

Question 3.
Refer to Monitoring Progress Question 2. Use the equation of the line of best fit to predict the attendance at the amusement park in 2017.

Question 4.
Is there a correlation between time spent playing video games and grade point average? If so, is there a causal relationship? Explain your reasoning.

Analyzing Lines of Fit 4.5 Exercises

Vocabulary and Core Concept Check

Question 1.
VOCABULARY
When is a residual positive? When is it negative?
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 1

Question 2.
WRITING
Explain how you can use residuals to determine how well a line of fit models a data set.
Answer:

Question 3.
VOCABULARY
Compare interpolation and extrapolation.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 3

Question 4.
WHICH ONE DOESN’T BELONG?
Which correlation coefficient does not belong with the other three? Explain your reasoning.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 89
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 5–8, use residuals to determine whether the model is a good fit for the data in the table. Explain.

Question 5.
y = 4x – 5
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 90
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 5.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 5.2

Question 6.
y = 6x + 4
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 91
Answer:

Question 7.
y = -1.3x + 1
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 92
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 7.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 7.2

Question 8.
y = -0.5x – 2
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 93
Answer:

Question 9.
ANALYZING RESIDUALS
The table shows the growth y (in inches) of an elk’s antlers during week x. The equation y = -0.7x + 6.8 models the data. Is the model a good fit? Explain.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 94
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 9

Question 10.
ANALYZING RESIDUALS
The table shows the approximate numbers y (in thousands) of movie tickets sold from January to June for a theater. In the table, x = 1 represents January. The equation y = 1.3x + 27 models the data. Is the model a good fit? Explain.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 95
Answer:

In Exercises 11–14, use a graphing calculator to find an equation of the line of best fit for the data. Identify and interpret the correlation coefficient.

Question 11.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 96
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 11

Question 12.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 97
Answer:

Question 13.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 98
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 13

Question 14.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 99
Answer:

ERROR ANALYSIS
In Exercises 15 and 16, describe and correct the error in interpreting the graphing calculator display.

Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 100

Question 15.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 101
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 15

Question 16.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 102
Answer:

Question 17.
MODELING WITH MATHEMATICS
The table shows the total numbers y of people who reported an earthquake x minutes after it ended.
a. Use a graphing calculator to find an equation of the line of best fit. Then plot the data and graph the equation in the same viewing window.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 103
b. Identify and interpret the correlation coefficient.
c. Interpret the slope and y-intercept of the line of best fit.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 17

Question 18.
MODELING WITH MATHEMATICS
The table shows the numbers y of people who volunteer at an animal shelter on each day x.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 104
a. Use a graphing calculator to find an equation of the line of best fit. Then plot the data and graph the equation in the same viewing window.
b. Identify and interpret the correlation coefficient.
c. Interpret the slope and y-intercept of the line of best fit.
Answer:

Question 19.
MODELING WITH MATHEMATICS
The table shows the mileages x (in thousands of miles) and the selling prices y (in thousands of dollars) of several used automobiles of the same year and model.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 105
a. Use a graphing calculator to find an equation of the line of best fit.
b. Identify and interpret the correlation coefficient.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 106
c. Interpret the slope and y-intercept of the line of best fit.
d. Approximate the mileage of an automobile that costs $15,500. e. Predict the price of an automobile with 6000 miles.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 19.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 19.2

Question 20.
MODELING WITH MATHEMATICS
The table shows the lengths x and costs y of several sailboats.
a. Use a graphing calculator to find an equation of the line of best fit.
b. Identify and interpret the correlation coefficient.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 107
c. Interpret the slope and y-intercept of the line of best fit.
d. Approximate the cost of a sailboat that is 20 feet long.
e. Predict the length of a sailboat that costs $147,000.
Answer:

In Exercises 21–24, tell whether a correlation is likely in the situation. If so, tell whether there is a causal relationship. Explain your reasoning.

Question 21.
the amount of time spent talking on a cell phone and the remaining battery life
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 21

Question 22.
the height of a toddler and the size of the toddler’s vocabulary
Answer:

Question 23.
the number of hats you own and the size of your head
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 23

Question 24.
the weight of a dog and the length of its tail
Answer:

Question 25.
OPEN-ENDED
Describe a data set that has a strong correlation but does not have a causal relationship.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 25

Question 26.
HOW DO YOU SEE IT?
Match each graph with its correlation coefficient. Explain your reasoning.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 108
Answer:

Question 27.
ANALYZING RELATIONSHIPS
The table shows the grade point averages y of several students and the numbers x of hours they spend watching television each week.
a. Use a graphing calculator to find an equation of the line of best fit. Identify and interpret the correlation coefficient.
b. Interpret the slope and y-intercept of the line of best fit.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 109
c. Another student watches about 14 hours of television each week. Approximate the student’s grade point average.
d. Do you think there is a causal relationship between time spent watching television and grade point average? Explain.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 27.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 27.2

Question 28.
MAKING AN ARGUMENT
A student spends 2 hours watching television each week and has a grade point average of 2.4. Your friend says including this information in the data set in Exercise 27 will weaken the correlation. Is your friend correct? Explain.
Answer:

Question 29.
USING MODELS
Refer to Exercise 17.
a. Predict the total numbers of people who reported an earthquake 9 minutes and 15 minutes after it ended.
b. The table shows the actual data. Describe the accuracy of your extrapolations in part (a).
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 110
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 29.1

Question 30.
THOUGHT PROVOKING
A data set consists of the numbers x of people at Beach 1 and the numbers y of people at Beach 2 recorded daily for 1 week. Sketch a possible graph of the data set. Describe the situation shown in the graph and give a possible correlation coefficient. Determine whether there is a causal relationship. Explain.
Answer:

Question 31.
COMPARING METHODS
The table shows the numbers y (in billions) of text messages sent each year in a five-year period, where x = 1 represents the first year in the five-year period.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 111
a. Use a graphing calculator to find an equation of the line of best fit. Identify and interpret the correlation coefficient.
b. Is there a causal relationship? Explain your reasoning.
c. Calculate the residuals. Then make a scatter plot of the residuals and interpret the results.
d. Compare the methods you used in parts (a) and (c) to determine whether the model is a good fit. Which method do you prefer? Explain.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 31.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 31.2
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 31.3

Maintaining Mathematical Proficiency

Determine whether the table represents a linear or nonlinear function. Explain. (Section 3.2)

Question 32.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 112
Answer:

Question 33.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 113
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.5 Question 33

Lesson 4.6 Arithmetic Sequences

Essential Question
How can you use an arithmetic sequence to describe a pattern?

An arithmetic sequence is an ordered list of numbers in which the difference between each pair of consecutive terms, or numbers in the list, is the same.

EXPLORATION 1
Describing a Pattern
Work with a partner.
Use the figures to complete the table. Plot the points given by your completed table. Describe the pattern of the y-values.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 114

Communicate Your Answer

Question 2.
How can you use an arithmetic sequence to describe a pattern? Give an example from real life.

Question 3.
In chemistry, water is called H2O because each molecule of water has two hydrogen atoms and one oxygen atom. Describe the pattern shown below. Use the pattern to determine the number of atoms in 23 molecules.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 115

4.6 Lesson

Monitoring Progress

Write the next three terms of the arithmetic sequence.

Question 1.
-12, 0, 12, 24, . . .

Question 2.
0.2, 0.6, 1, 1.4, . . .

Question 3.
4, 3\(\frac{3}{4}\), 3\(\frac{1}{2}\), 3\(\frac{1}{4}\)

Graph the arithmetic sequence. What do you notice?

Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 116

Question 4.
3, 6, 9, 12, . . .

Question 5.
4, 2, 0, -2, . . .

Question 6.
1, 0.8, 0.6, 0.4, . . .

Question 7.
Does the graph shown represent an arithmetic sequence? Explain.

Write an equation for the nth term of the arithmetic sequence. Then find a25.

Question 8.
4, 5, 6, 7, . . .

Question 9.
8, 16, 24, 32, . . .

Question 10.
1, 0, -1, -2, . . .

Question 11.
A carnival charges $2 for each game after you pay a $5 entry fee.
a. Write a function that represents the arithmetic sequence.
b. Graph the function.
c. How many games can you play when you take $29 to the carnival?
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 117

Arithmetic Sequences 4.6 Exercises

Vocabulary and Core Concept Check

Question 1.
WRITING
Describe the graph of an arithmetic sequence.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 1

Question 2.
DIFFERENT WORDS, SAME QUESTION
Consider the arithmetic sequence represented by the graph. Which is different? Find “both” answers.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 118
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3 and 4, write the next three terms of the arithmetic sequence.

Question 3.
First term: 2
Common difference: 13
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 3

Question 4.
First term: 18
Common difference: −6
Answer:

In Exercises 5−10, find the common difference of the arithmetic sequence.

Question 5.
13, 18, 23, 28, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 5

Question 6.
175, 150, 125, 100, . . .
Answer:

Question 7.
-16, -12, -8, -4, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 7

Question 8.
4, 3\(\frac{2}{3}\), 3\(\frac{1}{3}\), 3, . . .
Answer:

Question 9.
6.5, 5, 3.5, 2, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 9

Question 10.
-16, -7, 2, 11, . . .
Answer:

In Exercises 11−16, write the next three terms of the arithmetic sequence.

Question 11.
19, 22, 25, 28, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 11

Question 12.
1, 12, 23, 34, . . .
Answer:

Question 13.
16, 21, 26, 31, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 13

Question 14.
60, 30, 0, -30, . . .
Answer:

Question 15.
1.3, 1, 0.7, 0.4, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 15

Question 16.
\(\frac{5}{6}\), \(\frac{2}{3}\), \(\frac{1}{2}\), \(\frac{1}{3}\), . . .
Answer:

In Exercises 17−22, graph the arithmetic sequence.

Question 17.
4, 12, 20, 28, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 17

Question 18.
-15, 0, 15, 30, . . .
Answer:

Question 19.
−1, −3, −5, −7, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 19

Question 20.
2, 19, 36, 53, . . .
Answer:

Question 21.
0, 41\(\frac{1}{2}\), 9, 13\(\frac{1}{2}\), . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 21

Question 22.
6, 5.25, 4.5, 3.75, . . .
Answer:

In Exercises 23−26, determine whether the graph represents an arithmetic sequence. Explain.

Question 23.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 119
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 23

Question 24.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 120
Answer:

Question 25.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 121
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 25

Question 26.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 122
Answer:

In Exercises 27−30, determine whether the sequence is arithmetic. If so, find the common difference.

Question 27.
13, 26, 39, 52, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 27

Question 28.
5, 9, 14, 20, . . .29.
Answer:

Question 29.
48, 24, 12, 6, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 29

Question 30.
87, 81, 75, 69, . . .
Answer:

Question 31.
FINDING A PATTERN
Write a sequence that represents the number of smiley faces in each group. Is the sequence arithmetic? Explain.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 123
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 31

Question 32.
FINDING A PATTERN
Write a sequence that represents the sum of the numbers in each roll. Is the sequence arithmetic? Explain.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 124
Answer:

In Exercises 33−38, write an equation for the nth term of the arithmetic sequence. Then find a10.

Question 33.
-5, -4, -3, -2, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 33

Question 34.
-6, -9, -12, -15, . . .
Answer:

Question 35.
\(\frac{1}{2}\), 1, 1\(\frac{1}{2}\), 2, ……
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 35

Question 36.
100, 110, 120, 130, ….
Answer:

Question 37.
10, 0, -10, -20, ……
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 37

Question 38.
\(\frac{3}{7}\), \(\frac{4}{7}\), \(\frac{5}{7}\), \(\frac{6}{7}\), ………
Answer:

Question 39.
ERROR ANALYSIS
Describe and correct the error in finding the common difference of the arithmetic sequence.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 125
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 39

Question 40.
ERROR ANALYSIS
Describe and correct the error in writing an equation for the nth term of the arithmetic sequence.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 126
Answer:

Question 41.
NUMBER SENSE
The first term of an arithmetic sequence is 3. The common difference of the sequence is 1.5 times the first term. Write the next three terms of the sequence. Then graph the sequence.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 41

Question 42.
NUMBER SENSE
The first row of a dominoes display has 10 dominoes. Each row after the first has two more dominoes than the row before it. Write the first five terms of the sequence that represents the number of dominoes in each row. Then graph the sequence.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 127
Answer:

REPEATED REASONING
In Exercises 43 and 44, (a) draw the next three figures in the sequence and (b) describe the 20th figure in the sequence.

Question 43.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 128
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 43

Question 44.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 129
Answer:

Question 45.
MODELING WITH MATHEMATICS
The total number of babies born in a country each minute after midnight January 1st can be estimated by the sequence shown in the table. (See Example 5.)
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 130
a. Write a function that represents the arithmetic sequence.
b. Graph the function.
c. Estimate how many minutes after midnight January 1st it takes for 100 babies to be born.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 45.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 45.2

Question 46.
MODELING WITH MATHEMATICS
The amount of money a movie earns each week after its release can be approximated by the sequence shown in the graph.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 131
a. Write a function that represents the arithmetic sequence.
b. In what week does the movie earn $16 million?
c. How much money does the movie earn overall?
Answer:

MATHEMATICAL CONNECTIONS
In Exercises 47 and 48, each small square represents 1 square inch. Determine whether the areas of the figures form an arithmetic sequence. If so, write a function f that represents the arithmetic sequence and find f(30).

Question 47.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 132
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 47

Question 48.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 133
Answer:

Question 49.
REASONING
Is the domain of an arithmetic sequence discrete or continuous? Is the range of an arithmetic sequence discrete or continuous?
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 49

Question 50.
MAKING AN ARGUMENT
Your friend says that the range of a function that represents an arithmetic sequence always contains only positive numbers or only negative numbers. Your friend claims this is true because the domain is the set of positive integers and the output values either constantly increase or constantly decrease. Is your friend correct? Explain.
Answer:

Question 51.
OPEN-ENDED
Write the first four terms of two different arithmetic sequences with a common difference of -3. Write an equation for the nth term of each sequence.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 51

Question 52.
THOUGHT PROVOKING
Describe an arithmetic sequence that models the numbers of people in a real-life situation.
Answer:

Question 53.
REPEATED REASONING
Firewood is stacked in a pile. The bottom row has 20 logs, and the top row has 14 logs. Each row has one more log than the row above it. How many logs are in the pile?
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 53

Question 54.
HOW DO YOU SEE IT?
The bar graph shows the costs of advertising in a magazine.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 134
a. Does the graph represent an arithmetic sequence? Explain.
b. Explain how you would estimate the cost of a six-page advertisement in the magazine.
Answer:

Question 55.
REASONING
Write a function f that represents the arithmetic sequence shown in the mapping diagram.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 135
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 55

Question 56.
PROBLEM SOLVING
A train stops at a station every 12 minutes starting at 6:00 A.M. You arrive at the station at 7:29 A.M. How long must you wait for the train?
Answer:

Question 57.
ABSTRACT REASONING
Let x be a constant. Determine whether each sequence is an arithmetic sequence. Explain.
a. x + 6, 3x + 6, 5x + 6, 7x + 6, . . .
b. x + 1, 3x + 1, 9x + 1, 27x + 1, . . .
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 57.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 57.2

Maintaining Mathematical Proficiency

Solve the inequality. Graph the solution. (Section 2.2)

Question 58.
x + 8 ≥ -9
Answer:

Question 59.
15 < b – 4
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 59

Question 60.
t – 21 < -12
Answer:

Question 61.
7 + y ≤ 3
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 61

Graph the function. Compare the graph to the graph of f(x) = | x |. Describe the domain and range. (Section 3.7)

Question 62.
h(x) = 3 | x |
Answer:

Question 63.
v(x) = | x – 5 |
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 63

Question 64.
g(x) = | x | + 1
Answer:

Question 65.
r(x) = -2 | x |
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.6 Question 65

Lesson 4.7 Piecewise Functions

Essential Question 

How can you describe a function that is represented by more than on equation?

EXPLORATION 1
Writing Equations for a Function
Work with a partner.

a. Does the graph represent y as a function of x? Justify your conclusion.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 135.1
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 135.4
b. What is the value of the function when x = 0? How can you tell?
c. Write an equation that represents the values of the function when x ≤ 0.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 136
d. Write an equation that represents the values of the function when x > 0.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 137
e. Combine the results of parts (c) and (d) to write a single description of the function.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 138

EXPLORATION 2
Writing Equations for a Function
Work with a partner.

a. Does the graph represent y as a function of x? Justify your conclusion.
b. Describe the values of the function for the following intervals.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 139
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 140

Communicate Your Answer

Question 3.
How can you describe a function that is represented by more than one equation?

Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 141

Question 4.
Use two equations to describe the function represented by the graph.

4.7 Lesson

Monitoring Progress

Evaluate the function.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 142

Question 1.
f(-8)

Question 2.
f(-2)

Question 3.
f(0)

Question 4.
f(3)

Question 5.
f(5)

Question 6.
f(10)

Describe the domain and range.

Question 7.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 143

Question 8.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 144

Write a piecewise function for the graph.

Question 9.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 145

Question 10.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 146

Question 11.
A landscaper rents a wood chipper for 4 days. The rental company charges $100 for the first day and $50 for each additional day. Write and graph a step function that represents the relationship between the number x of days and the total cost y (in dollars) of renting the chipper.

Question 12.
WHAT IF? The reference beam originates at (3, 0) and reflects off a mirror at (5, 4).
a. Write an absolute value function that represents the path of the reference beam.
b. Write the function in part (a) as a piecewise function.

Piecewise Functions 4.7 Exercises

Vocabulary and Core Concept Check

Question 1.
VOCABULARY
Compare piecewise functions and step functions.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 1

Question 2.
WRITING
Use a graph to explain why you can write the absolute value function y = | x | as a piecewise function.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3–12, evaluate the function.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 500

Question 3.
f(-3)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 3

Question 4.
f(-2)
Answer:

Question 5.
f(0)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 5

Question 6.
f(5)
Answer:

Question 7.
g(-4)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 7

Question 8.
g(-1)
Answer:

Question 9.
g(0)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 9

Question 10.
g(1)
Answer:

Question 11.
g(2)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 11

Question 12.
g(5)
Answer:

Question 13.
MODELING WITH MATHEMATICS
On a trip, the total distance (in miles) you travel in x hours is represented by the piecewise function
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 147
How far do you travel in 4 hours?
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 13

Question 14.
MODELING WITH MATHEMATICS
The total cost (in dollars) of ordering x custom shirts is represented by the piecewise function
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 148
Determine the total cost of ordering 26 shirts.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 148.1
Answer:

In Exercises 15–20, graph the function. Describe the domain and range.

Question 15.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 149
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 15

Question 16.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 150
Answer:

Question 17.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 151
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 17

Question 18.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 152
Answer:

Question 19.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 153
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 19

Question 20.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 154
Answer:

Question 21.
ERROR ANALYSIS
Describe and correct the error in finding f(5) when Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 155.1
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 155
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 21

Question 22.
ERROR ANALYSIS
Describe and correct the error in graphing Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 157
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 158
Answer:

In Exercises 23–30, write a piecewise function for the graph.

Question 23.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 159
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 23

Question 24.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 160
Answer:

Question 25.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 161
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 25.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 25.2

Question 26.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 162
Answer:

Question 27.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 163
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 27.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 27.2

Question 28.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 164
Answer:

Question 29.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 165
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 29.1

Question 30.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 166
Answer:

In Exercises 31–34, graph the step function. Describe the domain and range.

Question 31.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 167
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 31

Question 32.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 168
Answer:

Question 33.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 169
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 33

Question 34.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 170
Answer:

Question 35.
MODELING WITH MATHEMATICS
The cost to join an intramural sports league is $180 per team and includes the first five team members. For each additional team member, there is a $30 fee. You plan to have nine people on your team. Write and graph a step function that represents the relationship between the number p of people on your team and the total cost of joining the league.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 35.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 35.2

Question 36.
MODELING WITH MATHEMATICS
The rates for a parking garage are shown. Write and graph a step function that represents the relationship between the number x of hours a car is parked in the garage and the total cost of parking in the garage for 1 day.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 171
Answer:

In Exercises 37–46, write the absolute value function as a piecewise function.

Question 37.
y = | x | + 1
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 37

Question 38.
y = | x | – 3
Answer:

Question 39.
y = | x – 2 |
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 39

Question 40.
y = | x + 5 |
Answer:

Question 41.
y = 2 | x + 3 |
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 41

Question 42.
y = 4 | x – 1 |
Answer:

Question 43.
y = -5 | x – 8 |
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 43

Question 44.
y = -3 | x + 6 |
Answer:

Question 45.
y = – | x – 3 | + 2
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 45

Question 46.
y = 7| x + 1 | – 5
Answer:

Question 47.
MODELING WITH MATHEMATICS
You are sitting on a boat on a lake. You can get a sunburn from the sunlight that hits you directly and also from the sunlight that reflects off the water.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 172
a. Write an absolute value function that represents the path of the sunlight that reflects off the water.
b. Write the function in part (a) as a piecewise function.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 47.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 47.2

Question 48.
MODELING WITH MATHEMATICS
You are trying to make a hole in one on the miniature golf green.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 173
a. Write an absolute value function that represents the path of the golf ball.
b. Write the function in part (a) as a piecewise function.
Answer:

Question 49.
REASONING
The piecewise function f consists of two linear “pieces.” The graph of f is shown.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 174
a. What is the value of f(-10)?
b. What is the value of f(8)?
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 49.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 49.2

Question 50.
CRITICAL THINKING
Describe how the graph of each piecewise function changes when < is replaced with ≤ and ≥ is replaced with >. Do the domain and range change? Explain.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 175
Answer:

Question 51.
USING STRUCTURE Graph
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 176
Describe the domain and range.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 51.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 51.2

Question 52.
HOW DO YOU SEE IT? The graph shows the total cost C of making x photocopies at a copy shop.
Big Ideas Math Algebra 1 Answer Key Chapter 4 Writing Linear Functions 177
a. Does it cost more money to make 100 photocopies or 101 photocopies? Explain.
b. You have $40 to make photocopies. Can you buy more than 500 photocopies? Explain.
Answer:

Question 53.
USING STRUCTURE
The output y of the greatest integer function is the greatest integer less than or equal to the input value x. This function is written as Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 204. Graph the function for -4 ≤ x < 4. Is it a piecewise function? a step function? Explain.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 53.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 53.2

Question 54.
THOUGHT PROVOKING
Explain why
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 205
does not represent a function. How can you redefine y so that it does represent a function?
Answer:

Question 55.
MAKING AN ARGUMENT
During a 9-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, 2 inches per hour for the next 6 hours, and 1 inch per hour for the final hour.
a. Write and graph a piecewise function that represents the depth of the snow during the snowstorm.
b. Your friend says 12 inches of snow accumulated during the storm. Is your friend correct? Explain.
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 55.1
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 55.2

Maintaining Mathematical Proficiency

Write the sentence as an inequality. Graph the inequality.(Section 2.5)

Question 56.
A number r is greater than -12 and no more than 13.
Answer:

Question 57.
A number t is less than or equal to 4 or no less than 18.Graph f and h. Describe the transformations from the graph of f to the graph of h.(Section 3.6)
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 57

Question 58.
f(x) = x; h(x) = 4x + 3
Answer:

Question 59.
f(x) = x; h(x) = -x – 8
Answer:
Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions 4.7 Question 59

Question 60.
f(x) = x; h(x) = –\(\frac{1}{2}\) + 5
Answer:

Writing Linear Functions Performance Task: Any Beginning

4.4–4.7 What Did You Learn?

Core Vocabulary

Section 4.4
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 179

Section 4.5
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 178

Section 4.6
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 181

Section 4.7
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 182

Mathematical Practices

Question 1.
What resources can you use to help you answer Exercise 17 on page 200?

Question 2.
What calculations are repeated in Exercises 11–16 on page 214? When finding a term such as a50, is there a general method or shortcut you can use instead of repeating calculations?

Question 3.
Describe the definitions you used when you explained your answer in Exercise 53 on page 224.

Performance Task

Any Beginning
With so many ways to represent a linear relationship, where do you start? Use what you know to move between equations, graphs, tables, and contexts.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 183
To explore the answers to this question and more, go to Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 206

Writing Linear Functions Chapter Review

Question 1.
Write an equation of the line in slope-intercept form.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 207

Question 2.
Write an equation in point-slope form of the line that passes through the point (4, 7) and has a slope of -1.

Write a linear function f with the given values.

Question 3.
f(10) = 5, f(2) = -3

Question 4.
f(3) = -4, f(5) = -4

Question 5.
f(6) = 8, f(9) = 3

Question 6.
Line a passes through (0, 4) and (4, 3).
Line b passes through (0, 1) and (4, 0).
Line c passes through (2, 0) and (4, 4).

Question 7.
Line a: 2x – 7y = 14
Line b: y = \(\frac{7}{2}\)x – 8
Line c: 2x + 7y = -21

Question 8.
Write an equation of the line that passes through (1, 5) and is parallel to the line y = -4x + 2.

Question 9.
Write an equation of the line that passes through (2, -3) and is perpendicular to the line y = -2x – 3

Question 10.
What is the roasting time for a 12-pound turkey?

Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 185

Question 11.
Write an equation that models the roasting time as a function of the weight of a turkey. Interpret the slope and y-intercept of the line of fit.

Question 12.
Make a scatter plot of the residuals to verify that the model in the example is a good fit.

Question 13.
Use the data in the example.
(a) Approximate the height of a student whose shoe size is 9.
(b) Predict the shoe size of a student whose height is 60 inches.

Question 14.
Is there a causal relationship in the data in the example? Explain.

write an equation for the nth term of the arithmetic sequence. Then find a30.

Question 15.
11, 10, 9, 8, …..

Question 16.
6, 12, 18, 24,….

Question 17.
-9, -6, -3, 0,….

Question 18.
Evaluate the function in the example when (a) x = 0 and (b) x = 5.

Graph the function. Describe the domain and range.

Question 19.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 186

Question 20.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 187

Write the absolute value function as a piecewise function.

Question 21.
y =| x | + 15

Question 22.
y = 4| x + 5 |

Question 23.
y = 2 | x + 2 | – 3

Question 24.
You are organizing a school fair and rent a popcorn machine for 3 days. The rental company charges $65 for the first day and $35 for each additional day. Write and graph a step function that represents the relationship between the number x of days and the total cost y (in dollars) of renting the popcorn machine.

Writing Linear Functions Chapter Test

Graph the function. Describe the domain and range.

Question 1.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 188

Question 2.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 189

Write an equation in slope-intercept form of the line with the given characteristics.

Question 3.
slope = \(\frac{2}{5}\) ; y-intercept = -7

Question 4.
passes through (0, 6) and (3, -3)

Question 5.
parallel to the line y = 3x – 1; passes through (-2, -8)

Question 6.
perpendicular to the line y = \(\frac{1}{4}\)x – 9; passes through (1, 1)

Write an equation in point-slope form of the line with the given characteristics.

Question 7.
slope = 10; passes through (6, 2)

Question 8.
passes through (-3, 2) and (6, -1)

Question 9.
The first row of an auditorium has 42 seats. Each row after the first has three more seats than the row before it.
a. Find the number of seats in Row 25.
b. Which row has 90 seats?

Question 10.
The table shows the amount x (in dollars) spent on advertising for a neighborhood festival and the attendance y of the festival for several years.
a. Make a scatter plot of the data. Describe the correlation.
b. Write an equation that models the attendance as a function of the amount spent on advertising.
c. Interpret the slope and y-intercept of the line of fit.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 190

Question 11.
Consider the data in the table in Exercise 10.
a. Use a graphing calculator to find an equation of the line of best fit.
b. Identify and interpret the correlation coefficient.
c. What would you expect the scatter plot of the residuals to look like?
d. Is there a causal relationship in the data? Explain your reasoning.
e. Predict the amount that must be spent on advertising to get 2000 people to attend the festival.

Question 12.
Let a, b, c, and d be constants. Determine which of the lines, if any, are parallel or perpendicular. Explain.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 191

Question 13.
Write a piecewise function defined by three equations that has a domain of all real numbers and a range of -3 < y ≤ 1.

Writing Linear Functions Cumulative Assessment

Question 1.
Which function represents the arithmetic sequence shown in the graph?
A. f(n) = 15 + 3n
B. f(n) = 4 – 3
C. f(n) = 27 – 3n
D. f(n) = 24 – 3n
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 192

Question 2.
Which of the inequalities are equivalent?
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 193

Question 3.
Complete the table for the four situations below. Explain your reasoning.
a. the price of a pair of pants and the number sold
b. the number of cell phones and the number of taxis in a city
c. a person’s IQ and the time it takes the person to run 50 meters
d. the amount of time spent studying and the score earned
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 194

Question 4.
Consider the function f(x) = x – 1. Select the functions that are shown in the graph. Explain your reasoning.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 195

Question 5.
Use the numbers to fill in values for m and b in the equation y = mx + b so that its graph passes through the points (6, 1) and (-2, -3).
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 196

Question 6.
Fill in the piecewise function with -, +, <, ≤, >, or ≥ so that the function is represented by the graph.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 197

Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 198

Question 7.
You claim that you can create a relation that is a function, and your friend claims that she can create a relation that is not a function. Using the given numbers, create a relation of five ordered pairs that supports your claim. What relation of five ordered pairs can your friend use to support her claim?
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 199

Question 8.
You have two coupons you can use at a restaurant. Write and solve an equation to determine how much your total bill must be for both coupons to save you the same amount of money.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 200

Question 9.
The table shows the daily high temperatures x (in degrees Fahrenheit) and the numbers y of frozen fruit bars sold on eight randomly selected days. The equation y = 3x – 50 models the data.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 201
a. Select the points that appear on a scatter plot of the residuals.
Big Ideas Math Answers Algebra 1 Chapter 4 Writing Linear Functions 202
b. Determine whether the model is a good fit for the data. Explain your reasoning.

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