11-1 Inverse Variation
Determine whether each table or equation represents an inverse or a direct variation. Explain.
15. x
2
3
4
5
y
−6
−9
−12
−15
ANSWER: Direct; y = −3x.
17. x
−5
−2
2
8
y
8
20
−20
−5
ANSWER: Inverse; xy = −40.
19. ANSWER: Inverse; xy =
.
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.
24. y = −6 when x = −3
ANSWER: xy = 18
eSolutions Manual - Powered by Cognero
26. y = −4 when x = 16
Page 1
21. 11-1ANSWER: Inverse Variation
Direct; y = 9x.
Assume that y varies inversely as x. Write an inverse variation equation that relates x and y. Then graph
the equation.
24. y = −6 when x = −3
ANSWER: xy = 18
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
29. If y = 5 when x = 6, find x when y = 2.
ANSWER: 15
30. If y = 4 when x = 14, find x when y = −5.
ANSWER: −11.2
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: eSolutions
9 ft Manual - Powered by Cognero
Page 2
35. MUSIC When under equal tension, the frequency of a vibrating string from a piano varies inversely with the string
30. If y = 4 when x = 14, find x when y = −5.
11-1ANSWER: Inverse Variation
−11.2
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
35. MUSIC When under equal tension, the frequency of a vibrating string from a piano varies inversely with the string
length. If a string that is 420 millimeters in length vibrates at a frequency of 523 cycles a second, at what frequency
will a 707-millimeter string vibrate?
ANSWER: approximately 311 cycles per second
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.
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.
eSolutions Manual - Powered by Cognero
Page 3