Find the Constant of Variation 9y=45x

$9 y = 45 x$

Divide each term in $9 y = 45 x$ by $9$ and simplify.

Divide each term in $9 y = 45 x$ by $9$ .

$\frac{9 y}{9} = \frac{45 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{45 x}{9}$

Divide $y$ by $1$ .

$y = \frac{45 x}{9}$

Simplify the right side.

Cancel the common factor of $45$ and $9$ .

Factor $9$ out of $45 x$ .

$y = \frac{9 (5 x)}{9}$

Cancel the common factors.

Factor $9$ out of $9$ .

$y = \frac{9 (5 x)}{9 (1)}$

Cancel the common factor.

$y = \frac{9 (5 x)}{9 \cdot 1}$

Rewrite the expression.

$y = \frac{5 x}{1}$

Divide $5 x$ by $1$ .

$y = 5 x$

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 $5$ .

$5$