Cop

yrig

ht ©

by H

olt,

Rin

ehar

t and

Win

ston

. All r

ight

s re

serv

ed.

N A ME _________________________________________________ CLASS _______________ D ATE ______________

Algebra 1 Reteaching Masters 57

Reteachin g5.4 The Slope-Intercept Form

◆Skill A Writing an equation of a line in slope-intercept form

Recall The slope-intercept form of a line is .↑ ↑

slope y-intercept

◆ Ex a m p leWrite an equation for each line.a. containing (0, 1) and with a slope of b. containing (3, ) and (9, 0)

◆ So l uti o na. The slope, m, is given as . The line contains (0, 1), so this point is the

y-intercept, or b is 1. Substituting these numbers into the equation gives.

b. First find the slope.

Then subtitute the coordinates of one of the given points into the equationand solve for b.

For the point (9, 0):

Substituting this number for b and for m into the equation gives

the equation .y !23x " 6

y ! mx # b23

b ! "60 ! 6 # b

0 !23

(9) # b

m !"4 " 03 " 9

!"4"6

!23

y ! "2x # 1

"2

"4"2

y ! mx # b

For eac h e q u ati o n , fi n d th e sl o p e a n d th e y-i nterce pt.

1 . ______________ 2. ______________ 3. ______________

Write a n e q u ati o n i n sl o p e-i nterce pt f orm f or eac h l i n e.

4. with a slope of 2 and a y-intercept of

5. containing (0, ) and with a slope of

Write a n e q u ati o n i n sl o p e-i nterce pt f orm f or th e l i n e th atc o nta i n s eac h p a ir o f p o i nts.

6. (1, 1) and (3, 5) _________________________ 7. (2, ) and ( , 5) _______________________

8. (2, 4) and ( , 1) _________________________ 9. (1, 0) and (3, 2) _______________________"4

"1"4

13

"3

"1

y ! "x #12

y !12x # 2y ! 3x " 1

Copyright ©

by Holt, R

inehart and Winston. All rights reserved.

N A ME _________________________________________________ CLASS _______________ D ATE ______________

58 Reteaching Masters Algebra 1

Write a n e q u ati o n i n sl o p e-i nterce pt f orm f or eac h l i n e gra p h e dbel o w.

1 0. 1 1. 1 2.

________________________ ________________________ ________________________

Adena charges $5 plus $3 an hour for babysitting.

1 3. Write an equation for the amount of money, y, that Adena can earn

by babysitting for x hours.

1 4. How much will Adena earn if she babysits for 5 hours?

1 5. How many hours will Adena have to babysit in order to earn $26?

x

y

Ox

y

O

◆Skill B Using the slope-intercept form to write equations of lines

Recall In the formula y = mx + b, m is the slope and b is the y-intercept.

slope

The y-intercept is the point where the line crosses the y-axis.

◆ Ex a m p leFind the equation for the graph.

◆ So l uti o nThe line crosses the y-axis at (0, 2), so .

Locate two points on the line and countin order to find the slope.

slope

The equation for the graph is .y ! "12x # 2

!riserun

! "24

! "12

b ! 2

!riserun !

difference in y-valuesdifference in x-values

x

y

O

rise

run

x

y

O

4.

5. 0

6.

7.

8. undefined

9.

1 0. 6.5; ; $78, $97.50

1 1. ; y ! x; 21, 20

Lesson 5.4

1. slope ! 3; y-intercept ! "1

2. slope ! ; y-intercept ! 2

3. slope ! "1; y-intercept !

4. y ! 2x " 1

5.

6.

7.

8.

9.

1 0.

1 1.

1 2.

1 3.

1 4. $20

1 5. 7

Lesson 5.5

1.

2. 2x " 3y ! 0

3.

4.

5. (0, "2); ("1, 0)

6. (0, "3); (2, 0)

7.

8. or

9. or

1 0.

1 1.

1 2.

1 3. Point-slope form is easier when you aregiven a point and the slope of a line. Slope-intercept form is easier when you aregiven the slope and the y-intercept of a line.

Lesson 5.6

1.

2. "3

3.

4. "4

23

"12

y !13x # 1

y ! "12x # 6

y !12x " 3

y # 1 !13

(x # 6)y " 2 !13

(x " 3)

y ! 2(x # 3)y " 6 ! 2x

y # 1 !12

(x " 4)

x

y

O

(0, –3)(0, –2)

(2, 0)(–1, 0)

3x –

2y = 6

2x + y = –2

6x " y ! 12

2x " 5y ! 5

5x " 10y ! 15

y ! 3x # 5

y ! "23x " 2

y ! "23x " 2

y ! 3x # 1

y ! x " 1

y !12x # 3

y ! "3x # 2

y ! 2x " 1

y !13x " 3

12

12

17

17

y ! 6.5x

45

32

95

45

ANSWERSC

opyright ©by H

olt, Rinehart and W

inston. All rights reserved.

186 Answers Algebra 1