reteaching 5.4t s -i f - tarantamath [licensed for non...
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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
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