Find the Equation that Relates x and y x=9 , y=-13/3

$x = 9$ , $y = - \frac{13}{3}$

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.

$y = k x$

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

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

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

$k = \frac{- \frac{13}{3}}{9}$

Multiply the numerator by the reciprocal of the denominator.

$k = - \frac{13}{3} \cdot \frac{1}{9}$

Multiply $- \frac{13}{3} \cdot \frac{1}{9}$ .

Multiply $\frac{1}{9}$ by $\frac{13}{3}$ .

$k = - \frac{13}{9 \cdot 3}$

Multiply $9$ by $3$ .

$k = - \frac{13}{27}$

Use the direct variation model to create the equation.

$y = k x$

Substitute the value of $k$ into the direct variation model.

$y = (- \frac{13}{27}) \cdot x$

Simplify the result to find the direct variation equation.

$y = - \frac{13 x}{27}$

Find the Equation that Relates x and y x=9 , y=-13/3

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