Find the Equation that Relates x and y y=6 , x=42

$y = 6$ , $x = 42$

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.

$k = \frac{6}{42}$

Step 4

Cancel the common factor of $6$ and $42$ .

Factor $6$ out of $6$ .

$k = \frac{6 (1)}{42}$

Cancel the common factors.

Factor $6$ out of $42$ .

$k = \frac{6 \cdot 1}{6 \cdot 7}$

Cancel the common factor.

$k = \frac{6 \cdot 1}{6 \cdot 7}$

Rewrite the expression.

$k = \frac{1}{7}$

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.

$y = (\frac{1}{7}) x$

Step 7

Simplify the result to find the direct variation equation.

$y = \frac{x}{7}$

Find the Equation that Relates x and y y=6 , x=42

Related Questions

Support LCMGCF.com by disabling your adblocker.