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

$- 4 x + 5 y = 0$

Step 1

Add $4 x$ to both sides of the equation.

$5 y = 4 x$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

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 $\frac{4}{5}$ .

$\frac{4}{5}$