Question:
Find the equation of a line whose inclination with the $x$-axis is $30^{\circ}$ and which passes through the point $(0,5)$.
Solution:
As angle is given so we have to find slope first given by m = tanθ
$m=\tan 30^{\circ}$
$\mathrm{m}=\frac{1}{\sqrt{3}}$
Now the line is passing through the point (0, 5).using slope - intercept form of the equation of the line, we will find the intercept
$y=m x+c$ ................(1)
$5=\frac{1}{\sqrt{3}}(0)+\mathrm{c} \Rightarrow \mathrm{c}=5$
Putting the value of c in equation (1),we have
$y=\frac{1}{\sqrt{3}} x+5$
$x-(\sqrt{3}) y+5 \sqrt{3}=0$
So, required equation of line is $x-(\sqrt{3}) y+5 \sqrt{3}=0$