11-1 Inverse Variation
Determine whether each table or equation represents an inverse or a direct variation. Explain.
14. x
1
2
5
6
y
30
15
6
5
ANSWER: Inverse; xy = 30.
15. x
2
3
4
5
y
−6
−9
−12
−15
ANSWER: Direct; y = −3x.
16. x
−4
−2
2
4
y
−2
−1
1
2
ANSWER: Direct; y =
.
17. x
−5
−2
2
8
y
8
20
−20
−5
ANSWER: Inverse; xy = −40.
18. 5x − y = 0
ANSWER: Direct; y = 5x.
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19. ANSWER: Page 1
18. 5x − y = 0
11-1ANSWER: Inverse Variation
Direct; y = 5x.
19. ANSWER: Inverse; xy =
.
20. x = 14y
ANSWER: Direct; y = k x.
21. ANSWER: Direct; y = 9x.
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
ANSWER: xy = 40
24. y = −6 when x = −3
ANSWER: xy = 18
26. y = −4 when x = 16
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xy = −64
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11-1 Inverse Variation
26. y = −4 when x = 16
ANSWER: xy = −64
Solve. Assume that y varies inversely as x.
28. If y = 12 when x = 3, find x when y = 6.
ANSWER: 6
30. If y = 4 when x = 14, find x when y = −5.
ANSWER: −11.2
32. If y = 15 when x = −2, find y when x = 3.
ANSWER: −10
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?
ANSWER: 9 ft
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.
ANSWER: Inverse; the cost per wig times the number of wigs equals the total amount they can spend, $20.
37. The Spring family buys several lemonades for $1.50 each.
ANSWER: Direct; the number of lemonades times the cost per lemonade equals the total cost. So the ratio
is a constant $1.50.
38. Nicole earns $14 for babysitting 2 hours, and $21 for babysitting 3 hours.
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Direct; the number of hours times the rate per hour equals the total pay. The ratio
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is a constant $7.
ANSWER: Direct; the number of lemonades times the cost per lemonade equals the total cost. So the ratio
11-1 Inverse Variation is a constant $1.50.
38. Nicole earns $14 for babysitting 2 hours, and $21 for babysitting 3 hours.
ANSWER: Direct; the number of hours times the rate per hour equals the total pay. The ratio
is a constant $7.
39. Thirty video game tokens are divided evenly among a group of friends.
ANSWER: Inverse; the number of friends times the number of tokens per person equals the constant 30.
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