PERIOD
DATE
NAME
Lesson 4 Homework Practice
Slope-Intercept
Form
State the slope a n d the y-intercept for the g r a p h of e a c h equation.
1. y =
4JC +
1
4; 1
4.y=^x-3
-|;-3
+ 5
- 3 ; 5
3. - x + y = 4
1; 4
5 . 3 ' + 3:c = - 7
-3;-7
6. y =
1; 2
2.y
= -3x
+ 2
G r a p h e a c h equation u s i n g the slope a n d the ^'-intercept.
7. y = -2x
+ 2
8.y+x
=
-3
y
0
1 = y - f
10. CAMPING T h e e n t r a n c e f e e t o t h e n a t i o n a l p a r k i s $ 1 5 .
A campsite fee i s $ 1 5 p e r n i g h t . T h e t o t a l cost y f o r a
c a m p i n g t r i p f o r jc n i g h t s c a n b e r e p r e s e n t e d b y
t h e e q u a t i o n y = 15a: + 1 5 .
y
oU
7n
/U
Dfin
U
/
/f
/
20 /
f
i^n
/
A(\
u U
a. G r a p h t h e e q u a t i o n .
i n
1 u
b . U s e t h e g r a p h t o find t h e t o t a l c o s t f o r 4 n i g h t s .
$75
o
1
2 3
5 6 7 8if
4
c. I n t e r p r e t t h e s l o p e a n d t h e y - i n t e r c e p t .
The slope represents the cost per night of camping;
The y-intercept, 15, represents the one-time
cost of the park entrance fee.
11. GEOMETRY U s e t h e d i a g r a m s h o w n .
80
uU
X+ y
= 90
\ I
<
\
on
C.\J
y = - X + 90
0
b. G r a p h t h e e q u a t i o n .
Course 3 • Chapter 3 E q u a t i o n s i n T w o V a r i a b l e s
•y=-x+90 /
40
a. W r i t e t h e e q u a t i o n i n s l o p e - i n t e r c e p t f o r m .
c. U s e t h e g r a p h t o find t h e v a l u e o f y i f = 3 0 .
K
60
20
40
s
\
60
s
80
PERIOD
DATE
NAME
Lesson 5 Homework Practice
Graph a Line Using Intercepts
State the x- a n d y-intercepts of e a c h function.
2.^x-Gy
1. -6x + 8 y = 2 4
x-intercept —4; y-intercept 3
3. -^x-^y
= 12
x-intercept 24; y-intercept - 3
4. -10a: - lOy = - 2 0
x-intercept -48; y-intercept - 3 6
5.
X + y =
= 18
1
x-lntercept 2; y-intercept 2
-x-y=^
6.
x-intercept 1; y-intercept 1
x-intercept —1-; y-intercept - i
s t a t e the x- a n d y-intercepts of e a c h function. T h e n g r a p h the
function.
7 . -4x + 2y = -8
i
y
i
4y
1 /
f(i
X
(0 , 9
lo
2, 0)-
' i-
0
=- 1 8
8. 6x-2y
( - 3,
I
f o
2
X
- 4 )I
X-intercept 2; y-intercept —4
x-intercept —3; y-lntercept 9
9 . FARMING M r . J e a n s r a i s e s c o w s a n d c h i c k e n s o n h i s f a r m .
A l t o g e t h e r , h i s cows a n d chickens h a v e 1 4 0 legs. T h i s c a n
b e r e p r e s e n t e d b y t h e f u n c t i o n 4x + 2y = 1 4 0 . G r a p h t h e
f u n c t i o n . T h e n i n t e r p r e t t h e x- a n d > ' - i n t e r c e p t s .
Sample answer: The x-intercept indicates that he
has 35 cows and no chickens. The y-intercept
indicates that he has 70 chickens and no cows.
1
'0)
\
\
\
\
1n
lU
O
»^
3b, 0 )
10
X
1 0 . MONEY M o n t y h a s a t o t a l o f $ 2 9 0 i n t e n d o l l a r a n d five d o l l a r b i l l s . T h i s c a n b e
r e p r e s e n t e d b y t h e f u n c t i o n IQx + S y = 2 9 0 . I n t e r p r e t t h e x- a n d ^ / - i n t e r c e p t s .
Sample answer: The x-intercept indicates that he has 29 ten dollar bills
and no five dollar bills. The y-intercept indicates that he has 58 five
dollar bills and no ten dollar bills.
Course 3 • Chapter 3 E q u a t i o n s i n T w o V a r i a b l e s
43
PERIOD
DATE
NAME
Lesson 6 Homework Practice
Write
Linear
Equations
Write a n equation i n point-slope form a n d slope-intercept form for e a c h line.
1. p a s s e s t h r o u g h ( — 5 , 6 ) , s l o p e = 3
2. passes t h r o u g h (6, —6), slope = 5
y + 6 = 5(x - 6)
y = 5x - 36
y - 6 = 3(x -I- 5)
y = 3x -f 21
3. p a s s e s t h r o u g h ( 0 , 1 ) a n d ( 2 , 5 )
4. passes t h r o u g h (—5,9 ) a n d ( 1 , 3 )
y - 9 = -1(x-h5)
y = - X -h 4
y - 5 = 2(x - 2)
y = 2x -h 1
5. passes t h r o u g h ( 1 , - 1 ) a n d ( 2 , 0 )
y+1
=1(X-1)
y = X—2
6. p a s s e s t h r o u g h ( - 3 , - 5 ) , s l o p e = 2
y -H 5 = 2(x -H 3)
y = 2x -H 1
Write the point-slope form of a n equation for e a c h l i n e g r a p h e d .
7. I I M I
I I I I
A
^
8. r T T T T l F
o
0
IT
- 4 - ; i-2
1
2 :
y - 1 = 4(x)
— / _ i 4
'X—^
ri
m
9 . TEMPERATURE T h e t a b l e s h o w s t h e t e m p e r a t u r e
at certain hours. Assuming the temperature change
is linear, w r i t e a n equation i n point-slope f o r m t o
r e p r e s e n t t h e t e m p e r a t u r e y atx h o u r .
y - 3 5 = 4(x-1)
1
y=-1(x-|-3)
2 3 4 x
Hour
Temperature
CF)
1
35
2
39
10. SPEED A f t e r 2 h o u r s , a c a r t r a v e l s 7 0 m i l e s . A f t e r 2 . 2 5 h o u r s i n t h e s a m e
trip, t h ecar travels 78.75 miles. W r i t e a n equation i npoint-slope f o r m t o
represent the distance y o f the car after x hours.
y - 70 = 35(x - 2)
Course 3 • Chapter 3 E q u a t i o n s i n T w o
Variables
47