Direct Variation

How to solve the direct variation problem: definition, 2 examples, and their solutions.

Definition

Definition, Formula

The direct variation is a relation
whose ratio of the variables, y/x, is constant, m:
y/x = m.

m is the constant of variation.

From y/x = m, multiply x on both sides.
Then y = mx.

This y = mx is the formula
that shows the direct variation.

Example 1

Example

x varies directly as y means
x and y show direct variation.

Solution

It says to find the constant of variation by comparing y to x.
This means the constant of variation, m, is y/x.

x = 2, y = 8
So m = 8/2.

8/2 = 4

So the constant of variation is 4.

This means the formula between x and y is
y = 4x.

Example 2

Example

Solution

First find the constant of variation.

x = 2, y = 4

So the constant of variation, m, is 4/2.

4/2 = 2
So m = 2.

The constant of variation, m, is 2.

So write the formula of the relation:
y = 2x.

x = 5, y = k
Put these into the formula y = 2x.
Then k = 2⋅5.

2⋅5 = 10

So k = 10 is the answer.