# Slope Intercept Form of Equation of Straight Line

Consider the straight line $l$. Let $P\left( {x,y} \right)$ be any point on the given line $l$. Suppose that $\alpha$ be the inclination of the line $l$ as shown in the given diagram, i.e. $\tan \alpha = m$
Take $c$ as a $Y$-intercept of the straight line because it cutting the $Y$-axis at the point $Q\left( {0,c} \right)$, i.e. $OQ = c = Y$-intercept.
From point $P$ draw $PM$ perpendicular on $X$-axis also from $Q$ draw $QR$ perpendicular on $PM$.

Now from the given diagram, consider the triangle $\Delta PQR$, i.e. $m\angle RQP = \alpha$, 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 Y-intercept $c$.

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

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

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

Which is the required equation of straight line.