Question

Find the equation of the line which is 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

Here, slope $m=\tan {30}^{\circ }=\frac{1}{\sqrt{3}}$
And $y$- intercept, $c=2$
We know that equation of line whose slope is $m$ and $y$- intercept $c$ is $y=mx+c$
$\therefore$ Equation of the line is
$\Rightarrow y=\frac{1}{\sqrt{3}}x+2$
$\Rightarrow y=\frac{x+2\sqrt{3}}{\sqrt{3}}$
$\Rightarrow \sqrt{3}y=x+2\sqrt{3}$
$\Rightarrow x-\sqrt{3}y+2\sqrt{3}=0$