Find the Constant of Variation 7y=21x

$7 y = 21 x$

Step 1

Divide each term in $7 y = 21 x$ by $7$ and simplify.

Divide each term in $7 y = 21 x$ by $7$ .

$\frac{7 y}{7} = \frac{21 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{21 x}{7}$

Divide $y$ by $1$ .

$y = \frac{21 x}{7}$

Simplify the right side.

Cancel the common factor of $21$ and $7$ .

Factor $7$ out of $21 x$ .

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

Cancel the common factors.

Factor $7$ out of $7$ .

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

Cancel the common factor.

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

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 $3$ .

$3$