# Converting Linear Equations in Standard Form to Slope Intercept Form

The general equation or standard equation of a straight line is given by

Where $a$ and $b$ are any constants and also either $a \ne 0$ or $b \ne 0$.
Now to convert this linear equation in standard form to slope intercept form, by definition slope-intercept is written as $y = mx + c$.
The procedure of converting standard form to slope intercept, take the standard equation and separate the variable $y$ on the left hand side as follows

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

Example: Convert the equation $2x + 5y - 6 = 0$ into slope intercept form.
We have equation of line in standard form is $2x + 5y - 6 = 0$

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