Variations - College Level

If y, x and z are variables and K is a non-zero constant, write the algebraic equation that represent each of the following:

a. y varies directly with x
b. y varies inversely to x
c. y varies jointly with x and z

Answer:
a. y = Kx
b. y = K / x
c. y = Kxz

Explanation:
Variation problems usually appear in sciences such as physics and chemistry.
There are two types of variations: direct and inverse. A combination of those relationships creates other variations such as joint.
In a direct variation, when one variable such as (x) increases, that causes the other variable (y) to increase also. The same happens when one decreases thus causing the other one to decrease.
Therefore, in a direct variation, a change in one variable results in the same change in the other variable.
In an inverse proportion, an increase in one variable will result in a decrease in the other and thus the name inverse.
Therefore in an inverse proportion a change in one variable causes the opposite to happen to the other.
A combination of variations occurs also. When one variable varies directly with two variables, we say that it varies jointly.

©Copyright 2007.Najwa S. Hirn. All rights reserved.