Find the Constant of Variation 2y=6x

$2 y = 6 x$

Step 1

Divide each term in $2 y = 6 x$ by $2$ and simplify.

Divide each term in $2 y = 6 x$ by $2$ .

$\frac{2 y}{2} = \frac{6 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6 x}{2}$

Divide $y$ by $1$ .

$y = \frac{6 x}{2}$

Simplify the right side.

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (3 x)}{2 (1)}$

Cancel the common factor.

$y = \frac{2 (3 x)}{2 \cdot 1}$

Rewrite the expression.

$y = \frac{3 x}{1}$

Divide $3 x$ by $1$ .

$y = 3 x$

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 $3$ .

$3$