Find the Constant of Variation 20y=4x

$20 y = 4 x$

Step 1

Divide each term in $20 y = 4 x$ by $20$ and simplify.

Divide each term in $20 y = 4 x$ by $20$ .

$\frac{20 y}{20} = \frac{4 x}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 y}{20} = \frac{4 x}{20}$

Divide $y$ by $1$ .

$y = \frac{4 x}{20}$

Simplify the right side.

Cancel the common factor of $4$ and $20$ .

Factor $4$ out of $4 x$ .

$y = \frac{4 (x)}{20}$

Cancel the common factors.

Factor $4$ out of $20$ .

$y = \frac{4 x}{4 \cdot 5}$

Cancel the common factor.

$y = \frac{4 x}{4 \cdot 5}$

Rewrite the expression.

$y = \frac{x}{5}$

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 $\frac{1}{5}$ .

$\frac{1}{5}$