Find the Constant of Variation 8y=16x

$8 y = 16 x$

Step 1

Divide each term in $8 y = 16 x$ by $8$ and simplify.

Divide each term in $8 y = 16 x$ by $8$ .

$\frac{8 y}{8} = \frac{16 x}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{16 x}{8}$

Divide $y$ by $1$ .

$y = \frac{16 x}{8}$

Simplify the right side.

Cancel the common factor of $16$ and $8$ .

Factor $8$ out of $16 x$ .

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

Cancel the common factors.

Factor $8$ out of $8$ .

$y = \frac{8 (2 x)}{8 (1)}$

Cancel the common factor.

$y = \frac{8 (2 x)}{8 \cdot 1}$

Rewrite the expression.

$y = \frac{2 x}{1}$

Divide $2 x$ by $1$ .

$y = 2 x$

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 $2$ .

$2$