Question:
Find the equation of a line which cuts off intercept 5 on the x - axis and makes an angle of 600 with the positive direction of the x - axis.
Solution:
As intercept is given i.e. c = 5 and angle given so first we will find slope of line.
$m=\tan \theta$
$m=\tan 60^{\circ} \Rightarrow \sqrt{3}$
Now using slope intercept form of the equation of a line
$y=m x+c$
$y=(\sqrt{3}) x+5$
$(\sqrt{3}) x-y+5=0$
So, the required equation of line is $(\sqrt{3}) x-y+5=0$