Precalculus Examples

$x = - \frac{1}{9}$ , $y = 1$

Step 1

When two variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other. The formula for direct variation is $y = k x$ , where $k$ is the constant of variation.

$y = k x$

Step 2

Solve the equation for $k$ , the constant of variation.

$k = \frac{y}{x}$

Step 3

Replace the variables $x$ and $y$ with the actual values.

$k = \frac{1}{- \frac{1}{9}}$

Step 4

Cancel the common factor of $1$ and $- 1$ .

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Step 4.1

Rewrite $1$ as $- 1 (- 1)$ .

$k = \frac{- 1 \cdot - 1}{- \frac{1}{9}}$

Step 4.2

Move the negative in front of the fraction.

$k = - \frac{1}{\frac{1}{9}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$k = - (1 \cdot 9)$

Step 6

Multiply $- (1 \cdot 9)$ .

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Step 6.1

Multiply $9$ by $1$ .

$k = - 1 \cdot 9$

Step 6.2

Multiply $- 1$ by $9$ .

$k = - 9$