Solve for a ax+by+c=0

$a x + b y + c = 0$

Step 1

Move all terms not containing $a$ to the right side of the equation.

Subtract $b y$ from both sides of the equation.

$a x + c = - b y$

Subtract $c$ from both sides of the equation.

$a x = - b y - c$

Step 2

Divide each term in $a x = - b y - c$ by $x$ and simplify.

Divide each term in $a x = - b y - c$ by $x$ .

$\frac{a x}{x} = \frac{- b y}{x} + \frac{- c}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{a x}{x} = \frac{- b y}{x} + \frac{- c}{x}$

Divide $a$ by $1$ .

$a = \frac{- b y}{x} + \frac{- c}{x}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$a = - \frac{b y}{x} + \frac{- c}{x}$

Move the negative in front of the fraction.

$a = - \frac{b y}{x} - \frac{c}{x}$