Examples

$y = 1$ , $z = 1$ , $x = 8$

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 $y = k x z^{2}$ , where $k$ is the constant of variation.

$y = k x z^{2}$

Step 2

Solve the equation for $k$ , the constant of variation.

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

Step 3

Replace the variables $x$ , $y$ , and $z$ with the actual values.

$k = \frac{1}{(8) \cdot {(1)}^{2}}$

Step 4

One to any power is one.

$k = \frac{1}{8 \cdot 1}$

Step 5

Multiply $8$ by $1$ .

$k = \frac{1}{8}$

Step 6

Write the equation of variation such that $y = k x z^{2}$ , replacing $k$ with the $\frac{1}{8}$ .

$y = \frac{x z^{2}}{8}$

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