Find the Constant of Variation 2x-16y=0

$2 x - 16 y = 0$

Subtract $2 x$ from both sides of the equation.

$- 16 y = - 2 x$

Divide each term in $- 16 y = - 2 x$ by $- 16$ and simplify.

Divide each term in $- 16 y = - 2 x$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{- 2 x}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{- 2 x}{- 16}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{- 16}$

Simplify the right side.

Cancel the common factor of $- 2$ and $- 16$ .

Factor $- 2$ out of $- 2 x$ .

$y = \frac{- 2 (x)}{- 16}$

Cancel the common factors.

Factor $- 2$ out of $- 16$ .

$y = \frac{- 2 (x)}{- 2 (8)}$

Cancel the common factor.

$y = \frac{- 2 x}{- 2 \cdot 8}$

Rewrite the expression.

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

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 $\frac{1}{8}$ .

$\frac{1}{8}$