Find the Constant of Variation 20x-5y=0

$20 x - 5 y = 0$

Step 1

Subtract $20 x$ from both sides of the equation.

$- 5 y = - 20 x$

Step 2

Divide each term in $- 5 y = - 20 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 20 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 20 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 20 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{- 20 x}{- 5}$

Simplify the right side.

Cancel the common factor of $- 20$ and $- 5$ .

Factor $- 5$ out of $- 20 x$ .

$y = \frac{- 5 (4 x)}{- 5}$

Cancel the common factors.

Factor $- 5$ out of $- 5$ .

$y = \frac{- 5 (4 x)}{- 5 (1)}$

Cancel the common factor.

$y = \frac{- 5 (4 x)}{- 5 \cdot 1}$

Rewrite the expression.

$y = \frac{4 x}{1}$

Divide $4 x$ by $1$ .

$y = 4 x$

Step 3

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 $4$ .

$4$