# Direct Variation

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

## Definition

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.

## ExampleConstant of Variation

x varies directly as y means

x and y show direct variation.

It says

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.

## ExampleFind the y value

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.