Name: ____________________________________________________ Date: _______ Hour: ______
Direct and Inverse Variation WS
Linear Equation:
Direct Variation:
Inverse Variation:
Classify the following as direct, inverse, or linear.
1) y = –16x – 3 _____________
4) y =
9
x
7) y = 8x
_____________
_____________
2) y =
x
4
5) y = x + ½
8) y =
 .2
x
_____________
_____________
_____________
3) y = x
6) y =
_____________
x
_____________
9
9) y = 2.3x _____________
What is the constant of variation (k) for the following direct and inverse variations?
10) y = –8x ______
11) y =
 .2
______
x
12) y = x ______
Answer the following questions.
14) If x and y vary directly, as x increases what happens to the value of y?
15) If x and y vary inversely, as y decreases, what happens to the value of x?
16) If x and y vary directly, as y decreases, what happens to the value of x?
17) If x and y vary inversely, as x increases, what happens to the value of y?
13) y =
3 .5
______
x
Find the Missing Variable:
18) y varies directly with x. If y = 32 when x = -5, find y when x = -14.
19) y varies inversely with x. If y = 62 when x = 42, find x when y = -12.
20) y varies inversely with x. If y = 9 when x = -10, find y when x = 90.
21) y varies directly with x. If y = 1 when x = -4, find y when x = 12.
22) The population of a certain species of bacteria varies directly with the temperature. When the
temperature is 35 degrees Celsius, there are 7 million bacteria. How many millions of bacteria are there
when the temperature is 38 degrees Celsius?
23) The volume of a gas varies inversely with the pressure on it.
If the volume is 300 cm3 under a pressure of 48 kg/cm2, what is the volume under a pressure of 25
kg/cm2?
24) In kick boxing, it is found that the force needed to break a board, varies inversely with the length of
the board. If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it
take to break a board that is 6 feet long?
25) In scuba diving, the time it takes a diver to ascend safely to the surface varies directly with the
depth of the dive. It takes a minimum of 3 minutes from a safe ascent from 12 feet. Determine the
minimum time for a safe ascent from 1000 feet?