Find the Equation that Relates x and y x=20 y=10

$x = 20$ $y = 10$

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.

$k = \frac{10}{20}$

Cancel the common factor of $10$ and $20$ .

Factor $10$ out of $10$ .

$k = \frac{10 (1)}{20}$

Cancel the common factors.

Factor $10$ out of $20$ .

$k = \frac{10 \cdot 1}{10 \cdot 2}$

Cancel the common factor.

$k = \frac{10 \cdot 1}{10 \cdot 2}$

Rewrite the expression.

$k = \frac{1}{2}$

Use the direct variation model to create the equation.

$y = k x$

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

$y = (\frac{1}{2}) x$

Simplify the result to find the direct variation equation.

$y = \frac{x}{2}$

Find the Equation that Relates x and y x=20 y=10

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