Find the Constant of Variation -y/4=2x

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

Step 1

Multiply both sides of the equation by $- 4$ .

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

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{y}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{y}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- y}{4} = - 4 (2 x)$

Cancel the common factor.

$4 \cdot - 1 \frac{- y}{4} = - 4 (2 x)$

Rewrite the expression.

$- - y = - 4 (2 x)$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 4 (2 x)$

Multiply $y$ by $1$ .

$y = - 4 (2 x)$

Simplify the right side.

Multiply $2$ by $- 4$ .

$y = - 8 x$

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 $- 8$ .

$- 8$