Algebra I Part 1
Inverse Variation
P. 674-675: 14-32 (Even), 34, 36-39, 44, 49, 52
Name: _______________________________
Determine whether each table or equation represents an inverse or a direct variation. Explain.
14.
16.
X Y
1 30
2 15
5 6
6 5
18. 5x – y = 0
X Y
-4 -2
-2 -1
2 1
4 2
20. x = 14y
Assume that y varies inversely as x. Write an inverse variation equation that relates x and y. Then graph the
equation.
22. y = 2 when x = 20
10
24. y = -6 when x = -3
10
y
26. y = -4 when x = 16
10
y
8
8
8
6
6
6
4
4
4
2
2
2
x
-10 -8 -6 -4 -2
-2
2
4
6
8
10
y
x
-10 -8 -6 -4 -2
-2
2
4
6
8
10
x
-10 -8 -6 -4 -2
-2
-4
-4
-4
-6
-6
-6
-8
-8
-8
-10
-10
-10
2
4
6
8
10
Solve. Assume that y varies inversely as x.
28. If y = 12 when x = 3, find x when y = 6.
30. If y = 4 when x = 14, find x when y = -5.
32. If y = 15 when x = -2, find y when x = 3.
34. EARTH SCIENCE The water level in a river varies inversely with air temperature. When the air
temperature was 90° Fahrenheit, the water level was 11 feet. If the air temperature was 110° Fahrenheit,
what was the level of water in the river?
Determine whether each situation is an example of an inverse or a direct variation. Justify your reasoning.
36. The drama club can afford to purchase 10 wigs at $2 each or 5 wigs at $4 each.
37. The Spring family buys several lemonades for $1.50 each.
38. Nicole earns $14 for babysitting 2 hours, and $21 for babysitting 3 hours.
39. Thirty video game tokens are divided evenly among a group of friends.
44. PHYSICAL SCIENCE When two people are balanced on a seesaw, their distances from the center of the
seesaw are inversely proportional to their weights. If a 118-pound person sits 1.8 meters from the center
of the seesaw, how far should a 125-pound person sit from the center to balance the seesaw?
49. SWIMMING Logan and Brianna each bought a pool membership. Their average cost per day is inversely
proportional to the number of days that they go to the pool. Logan went to the pool 25 days for an
average cost per day of $5.60. Brianna went to the pool 35 days. What was her average cost per day?
52. ERROR ANALYSIS Christian and Trevor found an equation such that x and y vary inversely, and y = 10
when x = 5. Is either of them correct? Explain.