Find the Constant of Variation 4x=-y

$4 x = - y$

Step 1

Rewrite the equation as $- y = 4 x$ .

$- y = 4 x$

Step 2

Divide each term in $- y = 4 x$ by $- 1$ and simplify.

Divide each term in $- y = 4 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{4 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{4 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{4 x}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{4 x}{- 1}$ .

$y = - 1 \cdot (4 x)$

Rewrite $- 1 \cdot (4 x)$ as $- (4 x)$ .

$y = - (4 x)$

Multiply $4$ by $- 1$ .

$y = - 4 x$

Step 3

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 $- 4$ .

$- 4$