Examples

$y = 8$ , $x = 2$ , $z = - 7$

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.

$k = \frac{8}{(2) \cdot {(- 7)}^{2}}$

Step 4

Cancel the common factor of $8$ and $2$ .

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Step 4.1

Factor $2$ out of $8$ .

$k = \frac{2 \cdot 4}{2 \cdot {(- 7)}^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2 \cdot {(- 7)}^{2}$ .

$k = \frac{2 \cdot 4}{2 ({(- 7)}^{2})}$

Step 4.2.2

Cancel the common factor.

$k = \frac{2 \cdot 4}{2 {(- 7)}^{2}}$

Step 4.2.3

Rewrite the expression.

$k = \frac{4}{{(- 7)}^{2}}$

Step 5

Raise $- 7$ to the power of $2$ .

$k = \frac{4}{49}$

Step 6

Write the equation of variation such that $y = k x z^{2}$ , replacing $k$ with the $\frac{4}{49}$ .

$y = \frac{4 x z^{2}}{49}$

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