Name: __________________________________ Block: ______
Direct and Inverse Variation Review
Directions: Determine if each function represents an inverse or a direct variation. If so,
give the constant of variation. (Keep in mind, the answer may be neither.)
1.
x
2
8
32
y
16
4
1
4. 3y = 9x + 6
2. 4y = 3x
5.
x
20
15
10
3. y =
6.
y
10
7.5
5
12
𝑥
x
2
4
5
y
20
10
-8
Directions: Assume that x and y vary directly. Find the missing variable.
7. If y = 7 and x = 21, find x if y = 8.
8. If y = ½ and x = ¼, find y if x = 2.
Directions: Assume that x and y vary inversely. Find the missing variable.
9. If x = 3 and y = 3, find x when y = 9.
10. If x = 2 and y = ½, find y if x = 4.
Directions: Assuming that x and y vary directly, write the direct variation equation.
11. x = 9, y = 2
12.
x
y
1
-4
2
-8
3
-12
4
-16
Directions: Assuming that x and y vary inversely, write the inverse variation equation.
13. x = 6, y = ⅓
14.
x
y
1
12
2
6
3
4
4
3
Name: __________________________________ Block: ______
Directions: Decide if each of the graphs below represents direct variation. If so, state
the constant of variation.
15.
16.
Directions: Draw the graph of a function where y varies directly with x using the given
constant of variation.
17. Constant = 2
2
18. Constant = − 3
19. A theater company plans to hire people to build a stage set. The work time t (in
hours per person) varies inversely with the number of people hired p. The
company estimates that 25 people working for 300 hours each can complete the
job. Find the work time per person if the company hires 30 people.
20. According to Charles’s Law, the volume of a gas and its temperature vary directly
when the pressure remains constant. If the volume of the gas at 291 K was 152
mL, what is the volume of the gas at 305 K?
21. According to Boyle’s Law, the pressure and volume of a gas vary inversely if the
temperature is kept constant. If the gas has an initial volume of 2 L and a pressure
of 3 atm, find the pressure if the volume is decreased to 1.25 L.