F– Direct and Inverse Variation Test Review
Alg 1
Name:_________________________________
Date:________________B______________
Given that y varies directly with x, use the specified values to write a direct variation equation that relates x
and y. Then find y when x = 2
1. x = 4, y = 12
2. x = 24 y = -6
constant of variation= k = 3
constant of variation= k = ¼
equation: y = 3x
equation: y = ¼ x
new point: (2,6)
new point: (2, ½ )
Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates
x and y. Then find y when x = 3.
3. x = 12 y = -2
4. x = 9 y = 4
constant of variation= k = -24
constant of variation= k = 36
equation: y = -24/x
equation: y = 36/x
new point: (3,-8)
new point: (3,12)
Given the graphs I, II and III:
I.
II.
5. Which one(s) show(s) direct variation. Select one answer.
A. I only
C. II only
B. I & II only
D. II & III only
III.
E. III only
F. I, II and III
Tell whether the table represents direct, inverse or no variation. If it does show variation, write the direct or inverse
variation equation.
6.
7.
X
2
3
4
5
6
y
6
9
12
15
18
Direct Variation: y = 3x
8.
x
-1
1
2
3
4
y
12
-12
-6
-4
-3
Inverse Variation: y = -12/x
x
5
10
15
20
25
y
75
7.5
5
3.75
3
Neither
For #9 & #10, set up an direct or inverse variation equation. Find the constant of variation. Write the
equation. Find the new point.
9. The distance traveled in a given time on Interstate 66 varies directly with the speed. Last week we
traveled 220 miles at 55 miles per hour. How many miles would we travel in the same time period if
we decreased our speed to 50 miles per hour?
y = distance, x = speed
220/55 = 4
y = 4x
200 miles
10. The amount of work time in hours (h) needed to prepare for the school play varies inversely with the
number of people working (p). Twenty five people working (p) can complete the job in 300 hours (h).
Write the inverse variation equation that relates h and p. Then find the how many hours it will take if there
are 30 people working.
Y= hours, x = people
Y = 7500/x
250 hours
11. Does the given chart show direct or inverse variation?
Explain why or why not.
INVERSE VARIATION- The product of each point is the same (36).