Question

Find the equation of a line making an angle of ${150}^{\circ }$ with the x-axis and cutting off an intercept 2 from y-axis.

Answer 1

$\text{The equation of the line having slope m}\text{and y-intercept (0, c) is given by :}y=mx+cNow,m=tan\left({150}^{\circ }\right)=\frac{-1}{\sqrt{3}}and\text{y-intercept is (0, 2)}\text{The required equation of line is}y=mx+c\Rightarrow y=\frac{-x}{\sqrt{3}}+2\Rightarrow \sqrt{3}-2\sqrt{3}+x=0\Rightarrow x+\sqrt{3}y=2\sqrt{3}$