Find the angle between the x-axis and the line joining the points
Question:

Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).

Solution:

The slope of the line joining the points $(3,-1)$ and $(4,-2)$ is $m=\frac{-2-(-1)}{4-3}=-2+1=-1$

Now, the inclination $(\theta)$ of the line joining the points $(3,-1)$ and $(4,-2)$ is given by

$\tan \theta=-1$

$\Rightarrow \theta=\left(90^{\circ}+45^{\circ}\right)=135^{\circ}$

Thus, the angle between the x-axis and the line joining the points (3, –1) and (4, –2) is $135^{\circ}$