Find the Equation that Relates x and y y=12 , x=15

$y = 12$ , $x = 15$

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.

$k = \frac{12}{15}$

Cancel the common factor of $12$ and $15$ .

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Factor $3$ out of $12$ .

$k = \frac{3 (4)}{15}$

Cancel the common factors.

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Factor $3$ out of $15$ .

$k = \frac{3 \cdot 4}{3 \cdot 5}$

Cancel the common factor.

$k = \frac{3 \cdot 4}{3 \cdot 5}$

Rewrite the expression.

$k = \frac{4}{5}$

Use the direct variation model to create the equation.

$y = k x$

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

$y = (\frac{4}{5}) x$

Simplify the result to find the direct variation equation.

$y = \frac{4 x}{5}$

Find the Equation that Relates x and y y=12 , x=15

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