Question

Find the equation of the line intersecting the $y$-axis at a distance of $2$ units above the origin and making an angle of $30$ ${}^{\circ }$ with positive direction of the $x$-axis.

Answer 1

We know that if a line with slope $m$ makes $y$-intercept $c$, then equation of line is given as $y=mx+c$.
Here. we have given, $c=2$ and $m=\tan {30}^{\circ }=\frac{1}{\sqrt{3}}$
Thus the required equation of the given line is $y=\frac{1}{\sqrt{3}}x+2$
$\Rightarrow y=\frac{x+2\sqrt{3}}{\sqrt{3}}$
$\Rightarrow x-\sqrt{3}y+2\sqrt{3}=0$