Find the Slope and y-intercept Ax+By=C

$A x + B y = C$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$B y = C - A x$

Divide each term in $B y = C - A x$ by $B$ and simplify.

Divide each term in $B y = C - A x$ by $B$ .

$\frac{B y}{B} = \frac{C}{B} + \frac{- A x}{B}$

Simplify the left side.

Cancel the common factor of $B$ .

Cancel the common factor.

$\frac{B y}{B} = \frac{C}{B} + \frac{- A x}{B}$

Divide $y$ by $1$ .

$y = \frac{C}{B} + \frac{- A x}{B}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{C}{B} - \frac{A x}{B}$

Rewrite in slope-intercept form.

$y = \frac{1}{B} C - \frac{A x}{B}$

The equation is not linear, so a constant slope does not exist.

Not Linear