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

$x = - 4$ , $y = 6$

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.

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

Step 4

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

Factor $2$ out of $6$ .

$k = \frac{2 (3)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Move the negative in front of the fraction.

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

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.

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

Step 8

Simplify the result to find the direct variation equation.

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

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

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