Question

Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis.

Answer 1

It is known that if a line with slope m makes y-intercept c, then the equation of the line is given as
$y = mx + c$
Here, $c = 2$ and $m = tan \ 30°$ = $\frac {1}{\sqrt 3}$
Thus, the required equation of the given line is

$y=\frac {1}{\sqrt 3}x+2$

$y=\frac {x+2√3}{\sqrt 3}$

$\sqrt 3\ y=x+2\sqrt 3$

i.e, $x-\sqrt 3\ y+2\sqrt 3=0$