Find the Equation that Relates x and y x=12 , y=3

$x = 12$ , $y = 3$

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.

$k = \frac{3}{12}$

Step 4

Cancel the common factor of $3$ and $12$ .

Factor $3$ out of $3$ .

$k = \frac{3 (1)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$k = \frac{3 \cdot 1}{3 \cdot 4}$

Cancel the common factor.

$k = \frac{3 \cdot 1}{3 \cdot 4}$

Rewrite the expression.

$k = \frac{1}{4}$

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.

$y = (\frac{1}{4}) x$

Step 7

Simplify the result to find the direct variation equation.

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

Find the Equation that Relates x and y x=12 , y=3

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