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All rights reserved.

CHAPTER 4Writing Linear Functions

4.1 Writing Equations in Slope-Intercept Form ......................................................101 4.2 Writing Equations in Point-Slope Form ............................................................107 4.3 Writing Equations of Parallel and Perpendicular Lines ....................................113 4.4 Scatter Plots and Lines of Fit ...........................................................................119 4.5 Analyzing Lines of Fit ......................................................................................125 4.6 Arithmetic Sequences ......................................................................................131

100Copyright © Big Ideas Learning, LLCAll rights reserved.

Integrated Mathematics I Copyright © Big Ideas Learning, LLC Student Journal All rights reserved. 90

Chapter

4 Maintaining Mathematical Proficiency

Name _________________________________________________________ Date _________

Use the graph to answer the question.

1. What ordered pair corresponds to point A? 2. What ordered pair corresponds to point H?

3. What ordered pair corresponds to point E? 4. Which point is located in Quadrant III?

5. Which point is located in Quadrant IV? 6. Which point is located on the negative x-axis?

Solve the equation for y.

7. 12x y− = − 8. 8 4 16x y+ = 9. 3 5 15 0x y− + =

10. 0 3 6 12y x= − + 11. 2 3 4y x y− = + 12. 6 3 2y x x+ − =

13. Rectangle ABCD has vertices ( ) ( )4, 2 , 4, 5 ,A B− and ( )7, 5 .C What are the coordinates of vertex D?

x

y

2

4

−2

−4

42−2−4

A

B

E

FD

G C

H

−6

−6

6

6



Copyright © Big Ideas Learning, LLC Integrated Mathematics I All rights reserved. Student Journal

91

4.1 Writing Equations in Slope-Intercept FormFor use with Exploration 4.1

Name _________________________________________________________ Date __________

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

Go to BigIdeasMath.com for an interactive tool to investigate this exploration.

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.

a. b.

c. d.

1 EXPLORATION: Writing Equations in Slope-Intercept Form

−9

−6

6

9

(2, 3)

(0, −1)−9

−6

6

9

(0, 2)

(4, −2)

−9

−6

6

9

(−3, 3)

(3, −1)−9

−6

6

9

(2, −1)

(4, 0)



4.1 Writing Equations in Slope-Intercept Form (continued)

Name _________________________________________________________ Date _________

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.

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

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.

2 EXPLORATION: Mathematical Modeling

Smartphone Plan

Co

st p

er m

on

th(d

olla

rs)

020406080

100

Data usage (megabytes)5000 1000 1500 2000 2500 x

y




93

4.1 For use after Lesson 4.1

Name _________________________________________________________ Date __________

Notes:

Practice

Let (x1, y1) = (0, 3) and (x2, y2) = (4, 2).

m = y2 − y1 — x2 − x1

= 2 − 3 — 4 − 0

= −1 — 4

= − 1

— 4

Because the line crosses the y-axis at (0, 3), the y-intercept is 3.

So, the equation is y = − 1

— 4

x + 3.

Write f (−2) = 6 as (−2, 6) and f (0) = −4 as (0,−4). Find the slope of the line through these points.

m = −4 − 6 — 0 − (−2)

= −4 − 6 — 0 + 2

= −10 — 2

, or −5

Because the line crosses the y-axis at (0,−4), the y-intercept is −4.

y = mx + b

y = −5x − 4 A function is f (x) = −5x − 4.

Worked-Out Examples

Example #1

Example #2

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

Write a linear function f with the given values.

x

y

2

4

42

(0, 3)(4, 2)

( ) ( )f f− = = 2 6, 0 4−



4.1

Name _________________________________________________________ Date _________

Extra Practice In Exercises 1–6, write an equation of the line with the given slope and y-intercept.

1. slope: 0 2. slope: 1− 3. slope: 2 y-intercept: 9 y-intercept: 0 y-intercept: 3−

4. slope: 3− 5. slope: 4 6. slope: 13

y-intercept: 7 y-intercept: 2− y-intercept: 2

In Exercises 7–12, write an equation of the line in slope-intercept form.

7. 8. 9.

10. 11. 12.

x

y

2

−2

2−2

(−1, 3)

(0, −1) x

y

2

4

−2

−2

(2, 4)

2

(0, 0) x

y

2

−2

2−2

(2, 3)

(0, 1)

x

y

4

−4

4−4−4

(3, −4)

(0, 5)x

y1

−4

2 4−2

(−2,−3)(0, −2) x

y

2

4

−2

2 4−2

(0, 3)

(4, 0)

Practice A

Practice (continued)




95

4.1

Name _________________________________________________________ Date __________

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

13. ( ) ( )0, 4 , 8, 4− 14. ( ) ( )2,1 , 0, 7− 15. ( ) ( )0, 2 , 4, 3

16. ( ) ( )0, 5 , 4, 1− − − 17. ( ) ( )8, 0 , 0, 8 18. ( ) ( )0, 3 , 2, 5−

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

19. ( ) ( )0 5, 4 3f f= − = − 20. ( ) ( )5 5, 0 10f f− = = 21. ( ) ( )0 5, 9 4f f= = −

22. ( ) ( )0 10, 7 4f f= = − 23. ( ) ( )2 2, 0 2f f− = − = 24. ( ) ( )0 16, 2 8f f= =

25. An electrician charges an initial fee of $50 and $190 after 4 hours of work.

a. Write a linear model that represents the total cost as a function of the number of hours worked.

b. How much does the electrician charge per hour?

Practice (continued)


Integrated Mathematics I Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. 112

4.1 Practice B

Name _________________________________________________________ Date _________

In Exercises 1–3, write an equation of the line with the given slope and y-intercept.

1. slope: 3 2. slope: 0 3. slope: 25−

y-intercept: 9− y-intercept: 13 y-intercept: 7

In Exercises 4 and 5, write an equation of the line in slope-intercept form.

4. 5.

In Exercises 6–8, write an equation of the line that passes through the given points.

6. ( ) ( )4, 0 , 0, 7− 7. ( ) ( )0, 3 , 2.5, 2− − 8. ( ) ( )0, 4 , 6, 1.5−

In Exercises 9–11, write a linear function f with the given values.

9. ( ) ( )6 2, 0 5f f= − = − 10. ( ) ( )0 1, 2 1f f= − = − 11. ( ) ( )4 3, 0 2f f− = = −

12. A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each T-shirt printed with your design costs an additional $8.

a. Write a linear model that represents the total cost of purchasing your team’s T-shirts with your design as a function of the number of T-shirts.

b. Your team has 35 members. If a T-shirt is purchased for every member, what would be the cost?

13. Line is a reflection in the x-axis of line k. Write an equation that represents line k.

2

1(0, 0)

(−2, −3)−3

−2 x

y

4

2 (0, 2)

(3, −2)−2

x

y

2

(0, 2) (3, 2)

−2

−2 x

y

Practice B

chapter 4 writing linear functions - big ideas learning€¦ · chapter 4 writing linear functions...

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