Find the Constant of Variation 3y=18x

$3 y = 18 x$

Step 1

Divide each term in $3 y = 18 x$ by $3$ and simplify.

Divide each term in $3 y = 18 x$ by $3$ .

$\frac{3 y}{3} = \frac{18 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{18 x}{3}$

Divide $y$ by $1$ .

$y = \frac{18 x}{3}$

Simplify the right side.

Cancel the common factor of $18$ and $3$ .

Factor $3$ out of $18 x$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{6 x}{1}$

Divide $6 x$ by $1$ .

$y = 6 x$

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 $6$ .

$6$