Name______________________________
Date: _________________ Block: _______
Mrs. Mistron
Direct Variation y = kx
“y varies directly with x, where a is the
constant of variation”
Circle the following equations that represent direct variation:
y = 2x
y= x+3
y= x
5y = - 4x
3y – 2 = x
EXAMPLE ONE FIND THE CONSTANT OF VARIATION
y varies directly as x. Find the constant of variation given the following (x, y)
a) (2, 6)
b) (1, 2)
Inverse Variation y =
“y varies inversely with x, where a is the
constant of variation”
c) (9, 6)
4=
EXAMPLE TWO WRITE AN INVERSE VARIATION EQUATION.
The variables x and y vary inversely. Write an equation to relate the variables then find
y when x = -2.
a) (4, 7)
b) (-3, 5)
EXAMPLE THREE INVERSE VARIATION MODELS
The number of songs you are able to store onto an iPod varies inversely with the
average size of the song. My iPod can store 2500 songs with an average song length of
4 MB.
a) Write a general formula for the number of songs, n, that will fit on iPod
b) How many songs will fit if the average length is 2 MB? 3MB? 5MB? What do
you notice about the number of songs as the size increases?
Joint Variation z = axy
“z varies jointly with x and y with constant of
variation a”
EXAMPLE FOUR WRITE A JOINT VARIATION EQUATION
z varies directly with x and y. Write the equation that relates the variables if z = - 75, x =
3, and y = -5. Then find z when x = 2 and y = 6
EXAMPLE SIX VARIATION MODELS

Kepler's third law of planetary motion states that the square of the time required
for a planet to make one revolution about the sun varies directly as the cube of
the average distance of the planet from the sun. If you assume that Mars is 1.5
times as far from the sun as is the earth, find the approximate length of a Martian
year.

The weight of a body varies inversely as the square of its distance from the center
of the earth. If the radius of the earth is 4000 miles, how much would a 200-pound
man weight 1000 miles above the surface of the earth?

Under certain conditions, the thrust T of a propeller varies jointly as the fourth
power of its diameter d and the square of the number n of revolutions per
second.

The number of hours h that it takes m men to assemble x machines varies directly
as the number of machines and inversely as the number of men. If four men can
assemble 12 machines in four hours, how many men are needed to assemble 36
machines in eight hours?
Homework Worksheet