Find the Equation that Relates x and y x=5/2 , y=18

$x = \frac{5}{2}$ , $y = 18$

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.

$k = \frac{18}{\frac{5}{2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$k = 18 (\frac{2}{5})$

Step 5

Multiply $18 (\frac{2}{5})$ .

Combine $18$ and $\frac{2}{5}$ .

$k = \frac{18 \cdot 2}{5}$

Multiply $18$ by $2$ .

$k = \frac{36}{5}$

Step 6

Use the direct variation model to create the equation.

$y = k x$

Step 7

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

$y = (\frac{36}{5}) x$

Step 8

Simplify the result to find the direct variation equation.

$y = \frac{36 x}{5}$

Find the Equation that Relates x and y x=5/2 , y=18

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