# How do I change an Ax+By=C equation to a y=mx+b equation where m is the slope and b is the y intercept like 4x+2y=8?

Mar 21, 2018

$y = \left(- \frac{A}{B}\right) x + \frac{C}{A}$

#### Explanation:

If
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$
then
after subtracting $A x$ from both sides:
$\textcolor{w h i t e}{\text{XXX}} B y = - A x + C$
then dividing both sides by $B$
$\textcolor{w h i t e}{\text{XXX}} y = \left(- \frac{A}{B}\right) x + \frac{C}{A}$
which is the slope-intercept form with
$\textcolor{w h i t e}{\text{XXX}}$slope$= \left(- \frac{A}{B}\right)$
and
$\textcolor{w h i t e}{\text{XXX}}$y-intercept$= \left(\frac{C}{A}\right)$

Mar 21, 2018

$y = - 2 x + 4$

#### Explanation:

$\text{Rearrange "4x+2y=8" into required form}$

$\text{subtract "4x" from both sides}$

$\cancel{4 x} \cancel{- 4 x} + 2 y = - 4 x + 8$

$\Rightarrow 2 y = - 4 x + 8$

$\text{divide all terms by 2}$

$\frac{\cancel{2} y}{\cancel{2}} = \frac{- 4}{2} x + \frac{8}{2}$

$\Rightarrow y = - 2 x + 4 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$