Algebra I
Direct and Inverse Variation Practice
Name _____________________
Date _____________ Block ___
Tell whether the equation represents direct variation, inverse variation or neither.
1. y = -4x
y
=4
x
4.
3. x = 7y
5. 3x + 4y = 8
6. 2xy = 20
8. 3 x 
7. x = -8
For each problem find:
2. xy = 7
12
y
a) the direct variation
9. y = x + 7
b) the inverse variation
10. If y = 21 when x = 10, find y when x = 4.
Direct:
Inverse:
11. If y = 17.5 when x = 12, find y when x = 8.
Direct:
Inverse:
12. To travel a fixed distance, the rate is inversely proportional to the time required. When the rate is
60 miles per hour, the time required is 4 hours. What time would be required for the same distance if
the rate were increased to 80 miles per hour?
13. Tell if the graph is direct, inverse, or neither?
x
y
1 2 3 4 5
3 6 9 12 15
__________________
x 1 2 3 4 5
y 2 4 9 16 25
__________________
x
y
1 2 3 4 6
24 12 8 6 4
__________________
14. Which equation represents an
inverse variation?
18. If m varies directly as p, and m = 5
when p = 7, what is the constant of
variation?
a
b
=
4
9
a
2
B
=
5
b
C 2a + 3 = 4b + 3
a
D =7
b
A
15. Which of these equations is a direct
variation?
F
G
H
J
y = -8
y = -8x
y = -8x + 1
y = -8x – 1
16. If y varies directly as x and the constant of
variation is -2, which equation represents this
relationship?
A y = -2x
2
B y= 
x
x
C y= 
2
D y = 2x
17. A farmer pumps water from an irrigation well to water
his field. The time it takes to water the field varies
inversely with the rate at which the pump operates. It
takes 20 hours to water the field when the pumping rate is
600 gallons per minute. If he adjusts the pump so that it
pumps at a rate of 400 gallons per minute, how long will
it take to water the field?
F 12.5 hours
G 15 hours
H 30 hours
J 40 hours
A 35
B 12
7
C
5
5
D
7
19.