Find the Constant of Variation 16y=2x

$16 y = 2 x$

Step 1

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 $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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 $\frac{1}{8}$ .

$\frac{1}{8}$