Find the Constant of Variation 5x-4y=0

$5 x - 4 y = 0$

Step 1

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

$- 4 y = - 5 x$

Step 2

Divide each term in $- 4 y = - 5 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 5 x$ by $- 4$ .

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

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 $\frac{5}{4}$ .

$\frac{5}{4}$