Question

Find the equations of the lines for which $\tan \theta =\frac{2}{3}$, where $\theta$ is the angle of inclination of the line and $y-$ intercept is $\frac{-4}{3}$

Answer 1

Slope of the line is $m=\tan \theta =\frac{2}{32}$

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

$y=\frac{2}{3}x+\frac{-4}{3}$

$\Rightarrow 3y=2x-4$

$\therefore$equation of the line is $2x-3y-4=0$