# Equation of a Line with X Intercept

Consider the straight line $l$ and $\alpha$ be the inclination of the straight line as shown in the given diagram now the slope of the represented by $\tan \alpha = m$. Let $P\left( {x,y} \right)$ be any point on the given line $l$. Let $a$ be the X-intercept of the straight line, so the line must passes through the point $A\left( {a,0} \right)$.
Take $a$ as X-intercept of the straight line so the line must passes through the point $A\left( {a,0} \right)$, i.e. $OA = a =$X-intercept. From point $P$ draw $PQ$ perpendicular on $X$-axis.

Now from the given diagram, consider the triangle $\Delta PAQ$, i.e. $m\angle PAQ = \alpha$, by the definition of slope we take

Now by definition we can use $m$ instead of $\tan \alpha$, we get

Which is the equation of straight line having slope $m$ and X-intercept $a$.

NOTE: It may be noted that if the line passes through the origin $\left( {0,0} \right)$, then take X-intercept is equal to zero i.e. $a = 0$, so the equation of straight line becomes $y = mx$.

Example: Find the equation of straight line having slope $8$ and X-intercept is equal to$3$.
Here we have slope $m = 8$ and X-intercept $a = 3$
Now using the formula of straight line having slope and X-intercept

Substitute the above values in the formula to get the equation of straight line

Which is the required equation of straight line.