# Find the slope of the line which makes an angle of

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 $-\sqrt{3}$.