Find the Constant of Variation 3y=21x

$3 y = 21 x$

Step 1

Divide each term in $3 y = 21 x$ by $3$ and simplify.

Divide each term in $3 y = 21 x$ by $3$ .

$\frac{3 y}{3} = \frac{21 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{21 x}{3}$

Divide $y$ by $1$ .

$y = \frac{21 x}{3}$

Simplify the right side.

Cancel the common factor of $21$ and $3$ .

Factor $3$ out of $21 x$ .

$y = \frac{3 (7 x)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = \frac{3 (7 x)}{3 (1)}$

Cancel the common factor.

$y = \frac{3 (7 x)}{3 \cdot 1}$

Rewrite the expression.

$y = \frac{7 x}{1}$

Divide $7 x$ by $1$ .

$y = 7 x$

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 $7$ .

$7$