# Intercepts Form of a Line

If $a$ and $b$ are non-zero $X$ and $Y$ intercepts of a line $l$, then its equation is of the form

Since $a$ is a $X$-intercept of the line $l$, as we know that any point lies on the $X$-axis its value of $Y$ is equal to zero, so it passes through the point $A\left( {a,0} \right)$. Also if $b$ is the $Y$-intercept of the line $l$, and we know that any point lies on the $Y$-axis its value of $X$ is equal to zero, so it passes through the point $B\left( {0,b} \right)$ as shown in the given diagram.

Now to prove intercepts form of a line, use the formula for two points form of a straight line as given by

Take $A\left( {a,0} \right) = \left( {{x_1},{y_1}} \right)$ and $B\left( {0,b} \right) = \left( {{x_2},{y_2}} \right)$, putting these values in the above formula as

Which is the required equation of straight line in intercepts form.

Example: Find the equation of straight with $X$-intercept $A\left( {3,0} \right)$ and $Y$-intercept $B\left( {0,2} \right)$.
From the above information we have $X$-intercept is $a = 3$ and $Y$-intercept is $b = 2$, now putting all these values in the formula of intercepts form as given

Which is the required equation of straight line.