Copyright © 2013 Pearson Education, Inc.

Section 3.5

Slope-Intercept Form

The line with slope m and y-intercept b is given by

y = mx + b,

the slope–intercept form of a line.

Slope-Intercept FormPage 205

Example

For the graph write the slope-intercept form of the line.

Solution

The graph intersects the y-axis at 0, so the y-intercept is 0.

The graph falls 3 units for each 1 unit increase in x, the slope is –3.

The slope intercept-form of the line is y = –3x .

Page 205

Example

Sketch a line with slope 3/4 and y-intercept −2. Write its slope-intercept form. SolutionThe y-intercept is (0, −2). Slope ¾ indicates that the graph rises 3 units for each 4 units run in x. The line passes through the point (4, 1).

32

4y x

Page 206

Find the slope and y-intercept of the line

a. y = 5x – 3m= 5y- intercept is (0, -3)

c. 7x + y = 6y = -7x + 6

Slope-Intercept Form

43

2 b. xy (0,4) isintercept -y and

3

2m

(0,6) isintercept -y and 7m

Page 206

Example

Write the y = 4 – 3x equation in slope-intercept form and then graph it.Solution

Plot the point (0, 4).The line falls 3 units for each 1 unit increase in x.

Page 206

xy 34

43 xy

Write the y = 1/2x-1 equation in slope-intercept form and then graph it.Solution

Plot the point (0, -1).The line rises 1 units for each 2 unit increase in x.

Example #46 Page 212

12

1 xy

Write the -2x-y = -2 equation in slope-intercept form and then graph it.Solution

Plot the point (0, 2).The line falls 2 units for each 1 unit increase in x.

Example #54 Page 212

22 yx

22

22

xy

xy

Example 5

Modeling cell phone costs: Roaming with a cell phone costs $5 for the initial connection and $0.50 per minute.

Solutiona. If someone talks for 23 minutes while roaming what is the charge?

b. Write the slope-intercept form that gives the cost of talking for x minutes.

c. If the charge is $8.50, how long did the person talk?

50.16$52350.0

55.0 xy

5.855.0 x

Page 207-8similar to #73 Homework

try #74

Example 5, cont.

Modeling cell phone costs: Roaming with a cell phone costs $5 for the initial connection and $0.50 per minute.

Solutionc. If the charge is $8.50, how long did the person talk?

Page 207-8similar to #73 Homework

try #74

5.855.0 x5.35.0 x

5.0

5.3x

7x Person can talk 7 minutes.

Example #74

Electrical Rates: Electrical service costs $8 per month plus $0.10 per kilowatt-hour of electricity used.

Solutiona.If the resident of an apartment uses 650 kilowatt-hours in 1 month, what is the charge?

b.Write an equation in slope-intercept form that gives the cost C.

c.If the monthly electrical bill for the apartment’s resident is $43, how many kilowatt-watt hours were used?

73$8)650(10.0

810.0 xC

Page 207-8similar to #73 Homework

Example #74, cont.

Modeling cell phone costs: Roaming with a cell phone costs $5 for the initial connection and $0.50 per minute.

Solutionc. If the monthly electrical bill for the apartment’s resident is $43, how many kilowatt-watt hours were used?

Page 207-8similar to #73 Homework

try #74

4381.0 x351.0 x

1.0

35x

350x 350 kilowatt-hours used.

Parallel and Perpendicular LinesPage 208-10

Example

Find the slope-intercept form of a line parallel to y = 3x + 1 and passing through the point (2, 1). Sketch a graph of each line.SolutionThe line has a slope of 3 any parallel line also has slope 3.Slope-intercept form: y = 3x + b. The value of b can be found by substituting the point (2, 1) into the equation. 3

1 3(2)

1 6

5

y x b

b

b

b

3 5 y x

Page 208-10

Show that the line passing through (4,2) and (6,6) is parallel to the line passing through (0,-2) and (1,0).

46

26

12

12

xx

yym

Parallel Lines

22

4

10

02

12

12

xx

yym

21

2

Page 208-10

Slopes are equal

Example

Find the slope-intercept form of a line passing through the origin that is perpendicular to each line. a. y = 4x b. Solutiona. The y-intercept is 0. Perpendicular line has a slope of

b. The y-intercept is 0. Perpendicular line has a slope of

23

5 y x

1.

4

1

4y x

5.

2

5

2y x

Page 208-10

Show that the line passing through (-1,4) and (3,2) is perpendicular to the line passing through (-2,-1) and (2,7).

31

24

12

12

xx

yym

Perpendicular Lines

2

1

4

2

22

71

12

12

xx

yym

1

2

4

8

11

2

2

1

Page 208-10

Example

Find the slope-intercept form of the line perpendicular to

and passing through the point (1, 0). Sketch each line in the same xy-plane.

Solution

A line perpendicular has slope –3.

The value of b can be found by substituting the point in the slope-intercept form.

11

3y x

3

0 3( 1)

0 3

3

y x b

b

b

b

3 3y x

Page 208-10

DONE

Objectives

• Basic Concepts

•Finding Slope-Intercept Form

• Parallel and Perpendicular Lines