Examples

$z = 9$ , $y = 10$ , $x = 5$

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.

$k = \frac{10}{(5) \cdot {(9)}^{2}}$

Step 4

Cancel the common factor of $10$ and $5$ .

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Step 4.1

Factor $5$ out of $10$ .

$k = \frac{5 \cdot 2}{5 \cdot {(9)}^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $5 \cdot {(9)}^{2}$ .

$k = \frac{5 \cdot 2}{5 ({(9)}^{2})}$

Step 4.2.2

Cancel the common factor.

$k = \frac{5 \cdot 2}{5 {(9)}^{2}}$

Step 4.2.3

Rewrite the expression.

$k = \frac{2}{{(9)}^{2}}$

Step 5

Raise $9$ to the power of $2$ .

$k = \frac{2}{81}$

Step 6

Write the equation of variation such that $y = k x z^{2}$ , replacing $k$ with the $\frac{2}{81}$ .

$y = \frac{2 x z^{2}}{81}$

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