# General Form of Equation of a Line

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 $b \ne 0$.

CASE – I: If $a \ne 0$ or $b = 0$, then the general equation or standard equation of straight line $ax + by + c = 0$ can be written of the form

Which is the equation of straight line parallel to $Y$-axis. Thus, the line is parallel to $Y$-axis if $b = 0$.

CASE – II: If $a = 0$ or $b \ne 0$, then the general equation or standard equation of straight line $ax + by + c = 0$ can be written of the form

Which is the equation of straight line parallel to $X$-axis. Thus, the line is parallel to $X$-axis if $a = 0$.

CASE – III: If $a \ne 0$ or $b \ne 0$, then the general equation or standard equation of straight line $ax + by + c = 0$ can be written of the form

Which is the equation of straight line in slope intercept form with slope is $- \frac{a}{b}$ and $y$-intercept is $- \frac{c}{b}$.