Find the Constant of Variation -32x+4y=0

$- 32 x + 4 y = 0$

Step 1

Add $32 x$ to both sides of the equation.

$4 y = 32 x$

Step 2

Divide each term in $4 y = 32 x$ by $4$ and simplify.

Divide each term in $4 y = 32 x$ by $4$ .

$\frac{4 y}{4} = \frac{32 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{32 x}{4}$

Divide $y$ by $1$ .

$y = \frac{32 x}{4}$

Simplify the right side.

Cancel the common factor of $32$ and $4$ .

Factor $4$ out of $32 x$ .

$y = \frac{4 (8 x)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = \frac{4 (8 x)}{4 (1)}$

Cancel the common factor.

$y = \frac{4 (8 x)}{4 \cdot 1}$

Rewrite the expression.

$y = \frac{8 x}{1}$

Divide $8 x$ by $1$ .

$y = 8 x$

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 $8$ .

$8$