# Converting Linear Equations in Standard Form to the Slope Intercept Form

The general equation or standard equation of a straight line is:
$ax + by + c = 0$

In which, $a$ and $b$ are constants and either $a \ne 0$ or $b \ne 0$.

Now to convert this linear equation in standard form to the slope intercept form, by definition the slope-intercept is written as $y = mx + c$.

To convert the standard form to the slope intercept form, take the standard equation and separate the variable $y$ on the left hand side as follows:

$\begin{gathered} ax + by + c = 0 \\ \Rightarrow by = – ax – c \\ \Rightarrow y = \frac{{ – ax – c}}{b} \\ \Rightarrow y = – \frac{a}{b}x – \frac{c}{b} \\ \end{gathered}$

Compare this equation with the slope intercept form $y = mx + c$ where the slope is $– \frac{a}{b}$ and the y-intercept is $– \frac{c}{b}$.

Example: Convert the equation $2x + 5y – 6 = 0$ into the slope intercept form.

The equation of the line in standard form is $2x + 5y – 6 = 0$
$\begin{gathered} \Rightarrow 5y = – 2x + 6 \\ \Rightarrow y = \frac{{ – 2x + 6}}{5} \\ \Rightarrow y = – \frac{2}{5}x + \frac{6}{5} \\ \end{gathered}$

Compare this with equation $y = – \frac{2}{5}x + \frac{6}{5}$ with the slope intercept form $y = mx + c$. Here the slope is $– \frac{2}{5}$ and the y-intercept $\frac{6}{5}$.