Find the Constant of Variation 6y=18x

$6 y = 18 x$

Step 1

Divide each term in $6 y = 18 x$ by $6$ and simplify.

Divide each term in $6 y = 18 x$ by $6$ .

$\frac{6 y}{6} = \frac{18 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{18 x}{6}$

Divide $y$ by $1$ .

$y = \frac{18 x}{6}$

Simplify the right side.

Cancel the common factor of $18$ and $6$ .

Factor $6$ out of $18 x$ .

$y = \frac{6 (3 x)}{6}$

Cancel the common factors.

Factor $6$ out of $6$ .

$y = \frac{6 (3 x)}{6 (1)}$

Cancel the common factor.

$y = \frac{6 (3 x)}{6 \cdot 1}$

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 $3$ .

$3$