Question:
Find the equation of the line whose inclination is $\frac{5 \pi}{6}$ and which makes an intercept of 6 units on the negative direction of the y - axis.
Solution:
Given:
$\theta=\frac{5 \pi}{6}$
$\therefore$ slope, $m=\tan \theta=\tan \frac{5 \pi}{6}=-\frac{1}{\sqrt{3}}$
The y - intercept is 6 units.
Formula to be used: y = mx + c where m is the slope of the line and c is the y - intercept.
The equation of the line is
$y=-\frac{1}{\sqrt{3}} x-6$
i.e. $\sqrt{3} y+x+6 \sqrt{3}=0$
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