Question

Find the equations of the lines for which $\tan \theta =\frac{1}{\sqrt{3}}$, where $\theta$ is the angle of inclination of the line and $y-$ intercept is $-1$

Answer 1

Slope of the line is $m=\tan \theta =\frac{1}{\sqrt{3}}$

Using slope-intercept form, the equation is $y=mx+c$

$y=\frac{1}{\sqrt{3}}x-1$

$\Rightarrow \sqrt{3}y=x-\sqrt{3}$

$\therefore$equation of the line is $x-\sqrt{3}y-\sqrt{3}=0$