Precalculus Examples

x = 9

$x = 9$ ,

y = 4

$y = 4$

Step 1

When two variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other. The formula for direct variation is

y = k x

$y = k x$ , where

k

$k$ is the constant of variation.

y = k x

$y = k x$

Step 2

Solve the equation for

k

$k$ , the constant of variation.

k = \frac{y}{x}

$k = \frac{y}{x}$

Step 3

Replace the variables

x

$x$ and

y

$y$ with the actual values.

k = \frac{4}{9}

$k = \frac{4}{9}$

Step 4

Use the direct variation model to create the equation.

y = k x

$y = k x$

Step 5

Substitute the value of

k

$k$ into the direct variation model.

y = (\frac{4}{9}) x

$y = (\frac{4}{9}) x$

Step 6

Simplify the result to find the direct variation equation.

y = \frac{4 x}{9}

$y = \frac{4 x}{9}$

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