Find the Constant of Variation 5y=10x

$5 y = 10 x$

Step 1

Divide each term in $5 y = 10 x$ by $5$ and simplify.

Divide each term in $5 y = 10 x$ by $5$ .

$\frac{5 y}{5} = \frac{10 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{10 x}{5}$

Divide $y$ by $1$ .

$y = \frac{10 x}{5}$

Simplify the right side.

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 x$ .

$y = \frac{5 (2 x)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = \frac{5 (2 x)}{5 (1)}$

Cancel the common factor.

$y = \frac{5 (2 x)}{5 \cdot 1}$

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 $2$ .

$2$