Find the Constant of Variation 5x-2y=0

$5 x - 2 y = 0$

Subtract $5 x$ from both sides of the equation.

$- 2 y = - 5 x$

Divide each term in $- 2 y = - 5 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 5 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 5 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 5 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 5 x}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{5 x}{2}$

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 $\frac{5}{2}$ .

$\frac{5}{2}$