Examples

$y = 7$ , $x = - 3$ , $z = - 1$

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.

$k = \frac{7}{(- 3) \cdot {(- 1)}^{2}}$

Step 4

Raise $- 1$ to the power of $2$ .

$k = \frac{7}{- 3 \cdot 1}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $- 3$ by $1$ .

$k = \frac{7}{- 3}$

Step 5.2

Move the negative in front of the fraction.

$k = - \frac{7}{3}$

Step 6

Write the equation of variation such that $y = k x z^{2}$ , replacing $k$ with the $- \frac{7}{3}$ .

$y = - \frac{7 z^{2} x}{3}$

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