Question

Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.

Answer 1

Here, $m=\tan {150}^{\circ }=-\tan {30}^{\circ }=-\frac{1}{\sqrt{3}}$
and c = y-intercept = 2

Substituting the values of m and c in y = mx + c, we get,

$$\begin{gathered} y=-\frac{1}{\sqrt{3}}x+2 \\ \Rightarrow x+\sqrt{3}y=2\sqrt{3} \end{gathered}$$

Hence, the equation of the required line is $x+\sqrt{3}y=2\sqrt{3}$.