Find the Equation that Relates x and y x=18 y=6

$x = 18$ $y = 6$

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.

$k = \frac{6}{18}$

Step 4

Cancel the common factor of $6$ and $18$ .

Factor $6$ out of $6$ .

$k = \frac{6 (1)}{18}$

Cancel the common factors.

Factor $6$ out of $18$ .

$k = \frac{6 \cdot 1}{6 \cdot 3}$

Cancel the common factor.

$k = \frac{6 \cdot 1}{6 \cdot 3}$

Rewrite the expression.

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

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.

$y = (\frac{1}{3}) x$

Step 7

Simplify the result to find the direct variation equation.

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

Find the Equation that Relates x and y x=18 y=6

Related Questions

Support LCMGCF.com by disabling your adblocker.