Examples

y = 1

$y = 1$ ,

x = 2

$x = 2$ ,

z = 3

$z = 3$

Step 1

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

y = k x z^{2}

$y = k x z^{2}$ , where

k

$k$ is the constant of variation.

y = k x z^{2}

$y = k x z^{2}$

Step 2

Solve the equation for

k

$k$ , the constant of variation.

k = \frac{y}{x z^{2}}

$k = \frac{y}{x z^{2}}$

Step 3

Replace the variables

x

$x$ ,

y

$y$ , and

z

$z$ with the actual values.

k = \frac{1}{(2) \cdot {(3)}^{2}}

$k = \frac{1}{(2) \cdot {(3)}^{2}}$

Step 4

Raise

3

$3$ to the power of

2

$2$ .

k = \frac{1}{2 \cdot 9}

$k = \frac{1}{2 \cdot 9}$

Step 5

Multiply

2

$2$ by

9

$9$ .

k = \frac{1}{18}

$k = \frac{1}{18}$

Step 6

Write the equation of variation such that

y = k x z^{2}

$y = k x z^{2}$ , replacing

k

$k$ with the

\frac{1}{18}

$\frac{1}{18}$ .

y = \frac{x z^{2}}{18}

$y = \frac{x z^{2}}{18}$

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