# Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin

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 $30^{\circ}$ with the positive direction of the $x$ axis.

Solution:

It is known that if a line with slope makes y-intercept c, then the equation of the line is given as

mx + c

Here, $c=2$ and $m=\tan 30^{\circ}=\frac{1}{\sqrt{3}}$.

Thus, the required equation of the given line is

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

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

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

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