Find the Constant of Variation -4y=8x

$- 4 y = 8 x$

Step 1

Divide each term in $- 4 y = 8 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 8 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{8 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{8 x}{- 4}$

Simplify the right side.

Cancel the common factor of $8$ and $- 4$ .

Factor $4$ out of $8 x$ .

$y = \frac{4 (2 x)}{- 4}$

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

$y = - 1 \cdot (2 x)$

Simplify the expression.

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y = - (2 x)$

Multiply $2$ by $- 1$ .

$y = - 2 x$

Step 2

Since the equation can be written in the form $y = k x$ , $y$ varies directly with $x$ and $k$ . The constant of variation, $k$ , is $- 2$ .

$- 2$