# Converting Linear Equations in Standard Form to the Intercepts Form

The general equation or standard equation of a straight line is:

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 intercepts form, i.e. $X$-intercept and $Y$-intercept, by definition the intercepts form is written as

To convert an equation from standard form to intercepts form, take the constant value $c$ and move it to the left hand side. Then divide both sides of the equation by $c$ and $1$ on the right hand side as follows:

Divide both sides of the above equation by  $- c$:

This is the equation of a line intercepts form with the $X$-intercept $- \frac{c}{a}$ and the $Y$-intercept $- \frac{c}{b}$.

Example: Convert the equation $2x + 5y - 6 = 0$ into the intercepts form.

We have the equation of a line in standard form as $2x + 5y - 6 = 0$

Compare with the intercepts form $\frac{x}{a} + \frac{y}{b} = 1$, where the $X$-intercept is $3$ and the $Y$-intercept is $\frac{6}{5}$.