Examples

y = 7

$y = 7$ ,

x = - 3

$x = - 3$ ,

z = - 1

$z = - 1$

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}

$y = k x z^{2}$ , 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{7}{(- 3) \cdot {(- 1)}^{2}}

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

Step 4

Raise

- 1

$- 1$ to the power of

2

$2$ .

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

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

Step 5

Simplify the expression.

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Step 5.1

Multiply

- 3

$- 3$ by

1

$1$ .

k = \frac{7}{- 3}

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

Step 5.2

Move the negative in front of the fraction.

k = - \frac{7}{3}

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

k = - \frac{7}{3}

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

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{7}{3}

$- \frac{7}{3}$ .

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

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

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