# Find the equation of a line passing through the origin and making an angle

Question:

Find the equation of a line passing through the origin and making an angle of $120^{\circ}$ with the positive direction of the $x$-axis.

Solution:

As angle is given so we have to find slope first give by m = tanθ

$\mathrm{m}=\tan 120^{\circ}$

$\mathrm{m}=\tan \left(180^{\circ}-60^{\circ}\right) \Rightarrow-\tan 60^{\circ}=-(\sqrt{3})$

( $\tan \left(180^{\circ}-\theta\right)$ is in II quadrant, $\tan x$ is negative)

Now equation of line passing through origin is given as y = mx

$y=-(\sqrt{3}) x$

$(\sqrt{3}) x+y=0$

So, required equation of line is $(\sqrt{3}) x+y=0$