Direct, Inverse & Joint Variation Worksheet
Section 8.1
Name:_________________
_____
Find the Missing Variable:
1) y varies directly with x. If y = -4 when x = 2, find y when x = -6.
2) y varies inversely with x. If y = 40 when x = 16, find x when y = -5.
3) y varies inversely with x. If y = 7 when x = -4, find y when x = 5.
4) y varies directly with x. If y = 15 when x = -18, find y when x = 1.6.
5) y varies directly with x. If y = 75 when x =25, find x when y = 25.
Classify the following as:
6) m = -5p
a) Direct
9) c =
b) Inverse
e
4
c) Neither
12) c = 3v
7) r =
9
t
10) n = ½ f
8) d = 4t
11) z =
13) u =
i
18
17) r =
9
t
 .2
t
What is the constant of variation for the following?
14) d = 4t
15) z =
 .2
t
16) n = ½ f
Answer the following questions.
18) If x and y vary directly, as x decreases, what happens to the value of y?
19) If x and y vary inversely, as y increases, what happens to the value of x?
20) If x and y vary directly, as y increases, what happens to the value of x?
21) If x and y vary inversely, as x decreases, what happens to the value of y?
Answer the following questions:
26) 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?
27) The volume V of gas varies inversely to the pressure P. The volume of a gas is 200
cm3 under pressure of 32 kg/cm2. What will be its volume under pressure of 40 kg/cm2?
28) 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 50 kg?
29) On a map, distance in km and distance in cm varies directly, and 25 km are
represented by 2cm. If two cities are 7cm apart on the map, what is the actual distance
between them?
30) 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?
Write an equation of joint variation to represent the situation and solve for the missing
information.
31) The cost c of materials for a deck varies jointly with the width w and the length l. If c
= $470.40 when w =12 and l =16, find the cost when w=10 and l = 25.
32) The value of real estate V varies jointly with the neighborhood index N and the
square footage of the house S. If V = $376, 320 when N = 96 and S =1600, find the value
of a property with N = 83 and S = 2150.
33) The number of gallons g in a circular swimming pool varies jointly with the square of
the radius r and the depth d. If g = 754 when r = 4 and d = 2, find the number of gallons
in the pool when r = 3 and d =1.5.
34) The strength of a rectangular beam varies jointly as its width and the square of it
depth. If the strength of a beam three inches wide by 10 inches deep is 1200 pounds per
square inch, what is the strength of a beam four inches wide and six inches deep?