Question:
Find the slope of the line which makes an angle of $30^{\circ}$ with the positive direction of the y-axis, measured anticlockwise.
Solution:
According to the given figure, the angle made by the line from X-axis is 90+30 $=120^{\circ}$
slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$
We also know that slope of a line is equal to tanθ, Where
$\theta=120^{\circ}$
$\tan \left(120^{\circ}\right)=\tan \left(90^{\circ}+30^{\circ}\right)=-\cot \left(30^{\circ}\right)=-\sqrt{3}$
Therefor the slope of the given line is $-\sqrt{3}$.