Math 2
Unit 6 – Direct and Inverse Variation
Name: ______________
Tell whether the table represents direct variation. If so, write the direct variation equation.
1.
2.
3.
x
0.5
y
9
x
8
y
7
x
-5
y
-2
3
54
2
28
3
1.2
-2
1
-36
18
-4
-0.5
7
-112
-2
10
-0.8
4
-8
-144
14
4
20
8
Given that y varies directly with x, use the specified values to write a direct variation equation
that relates x to y.
4.
5.
6.
7.
Given that y varies inversely with x, use the specified values to write an inverse variation equation
that relates x to y.
8.
9.
10.
11.
12. If y varies directly as x, and y = -8 when x = -2, find x when y = 32.
13. If y varies directly as x, and y = -4 when x = 2, find y when x = -6.
14. a varies inversely as z. If a = ¼ when z = 6, find z when a = 9.
15. y varies inversely with x. If y = 10 when x = -4, find y when x = 5.
Math 2
Unit 6 – Direct and Inverse Variation
Name: ______________
16. One way to keep moisture out of your basement is to paint the walls with waterproof paint. The
number gallons, g, of paint you need varies directly with the area A of the basement. One gallon of paint
covers 100 square feet.
a. Write a direct variation equation that relates g and A.
b. How many gallons do you need to cover 530 square feet?
17. The table shows the amount of time t (in seconds) it takes to download a file of size s (in kilobytes).
a. Explain why s varies directly with t.
Time, t(sec)
File size, s (kb)
b. Write a direct variation equation that relates s and t.
c. How long will it take to download an 800 kilobyte file?
Round your answer to the nearest second.
15
420
30
840
45
1260
Identify whether each situation can be modeled by direct variation, inverse variation, or neither.
18. Fred earns $6.50 per hour. _________________
19. Edwina earns $450 plus 7.5% commission on sales. ________________
20. A car travels 250 miles to Myrtle Beach; the faster the car goes, the less time the trip takes.
___________________
21. For his flooring business, Joe needs to convert feet to yards. _______________
22. The volume of water in a swimming pool as it is filed at a rate of 200 gallons per minute. _________
23. If the area of a rectangle remains constant and the width decreases, then the length increases
____________________
24. You purchase a new SUV, the resale price decreases _________________
Answer each of the following questions. Some are models of direct variation, some are models of
inverse variation.
25.The electric current I, is amperes, in a circuit varies directly as the voltage V. When 12 volts are
applied, the current is 4 amperes. What is the current when 18 volts are applied?
Math 2
Unit 6 – Direct and Inverse Variation
Name: ______________
26.The number of kilograms of water in a person’s body varies directly as the person’s mass. A
person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a
person with a mass of 150 kg?
27.The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If
the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?
28.The owner of an electronics store determines that the monthly demand for a computer varies
inversely with the price of the computer. When the price is $700, the monthly demand is 250
units. What is the monthly demand when the price is $500?
29.Your distance from lightning varies directly with the time it takes you to hear thunder. If
you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the
lightning.
a. Write a direct variation equation for the relationship between time and distance.
b. Estimate how many seconds it would take for the thunder to travel a distance of 4
miles.
30.For the Choir fundraiser, the number of tickets Allie can buy is inversely proportional to the price of
the tickets. She can afford 15 tickets that cost $5 each. How many tickets can Allie buy if each cost
$3?
31.The time it takes you to get to campus varies inversely as your driving speed. Averaging 20 miles per
hour in bad traffic, it takes you 1.5 hours to get to campus. How long would the trip take averaging 50
miles per hour?