Question

Find the equations of the lines for which $\cot \theta =\frac{1}{2}$, where $\theta$ is the angle of inclination of the line and $y-$ intercept is $\frac{-3}{2}$

Answer 1

Given:$\cot \theta =\frac{1}{2}\Rightarrow \tan \theta =\frac{1}{\cot \theta }=\frac{1}{2}$

Slope of the line is $m=\tan \theta =\frac{1}{2}$

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

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

$\Rightarrow 2y=x-3$

$\therefore$equation of the line is $x-2y-3=0$