Precalculus Examples

y = 3

$y = 3$ ,

x = 3

$x = 3$ ,

z = 7

$z = 7$

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}

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

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

Step 4

Cancel the common factor of

3

$3$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Raise

$7$ to the power of

$2$ .

$k = \frac{1}{49}$

Step 6

Write the equation of variation such that

$y = k x z^{2}$ , replacing

$k$ with the

$\frac{1}{49}$ .

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

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