Find the Equation that Relates x and y y=4 x=6

$y = 4$ $x = 6$

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.

$k = \frac{4}{6}$

Step 4

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$k = \frac{2 (2)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$k = \frac{2 \cdot 2}{2 \cdot 3}$

Cancel the common factor.

$k = \frac{2 \cdot 2}{2 \cdot 3}$

Rewrite the expression.

$k = \frac{2}{3}$

Step 5

Use the direct variation model to create the equation.

$y = k x$

Step 6

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

$y = (\frac{2}{3}) x$

Step 7

Simplify the result to find the direct variation equation.

$y = \frac{2 x}{3}$

Find the Equation that Relates x and y y=4 x=6

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