# Direct-Variation

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```					Direct Variation
Does the graph represent direct
variation?
y

4

3

2

1
-4   -3   -2   -1

x

-1           1   2   3   4

-2

-3

-4
NO
Which line represents direct
variation?
K
Does the graph represent direct
variation?
y

x
YES
Which equation represents direct
variation?
A     y = 2/3x + 5
B     y=5
C     y = 2/3x
D     x = 2/3
C
Which equation represents direct
variation?
A     y = -4x
B     y = -4x + 1
C     y = -4
D     x = -4
A
The amount of money earned on a job
varies directly to the number of hours
worked. If \$50.00 is earned in 8 hours,
how much is earned for 35 hours of
work?
M = kH

50.00 = 8k
6.25 = k
M = 6.25H
M = 6.25(35)
M = 218.75
50 x

8 35
• 8x = 50(35)
• 8x = 1750
• x = 1750/8
• x = 218.75

• \$218.75
A scale distance of 2.5 centimeters on
a certain map represents an actual
distance of 180 kilometers. If the
distance on the map varies directly with
the actual distance, what actual
distance does 6.5 centimeters
on the same map represent?
S = kA
2.5 = k(180)
1/72 = k
S = 1/72A
6.5 = 1/72A
468 = A
2.5 6.5

180   x
• 2.5x = 180(6.5)
• 2.5x = 1170
• x = 1170/2.5
• x = 468

• 468 kilometers
Mr. Johnstone used 15 gallons of gasoline
to drive 450 miles. If the amount of gasoline
used varies directly with the number of miles
driven. How far can he drive on a full tank of
20 gallons?
G = kM
15 = k(450)
1/30 = k
G = 1/30M
20 = 1/30M
600 = M
15 20

450 x
• 15x = 450(20)
• 15x = 9000
• x = 9000/15
• x = 600

• 600 miles
Mr. Parker drove 143 mi in 3.25 hours. If
the distance driven varies directly with the
amount of time, how far would he travel in 5
hours?
D = kT
143 = k(3.25)
44 = k
D = 44T
D = 44(5)
D = 220
143 x

3.25 5
• 3.25x = 143(5)
• 3.25x = 715
• x = 715/3.25
• x = 220

• 220 miles
Distance, d, varies directly as time, t,
when speed remains constant. If d is
240 miles when t is 8 hours, what is the
constant speed?
y = kx
• d = st
• 240 = 8s
• 240/8 = s
• 30 = s
If m varies directly as p, and m = 5
when p = 7, what is the constant of
variation?
y = kx
• m = kp
• 5 = 7k
• 5/7 = k
The number of calories, n, a person
burns varies directly with the amount
to time, t, spent running. If n = 275
when t = 22, what is the constant of
variation?
y = kx
• n = kt
• 275 = 22k
• 275/22 = k
• 12.5 = k
• 25/2 = k

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