Question

Find the equations of the lines for which $\tan \theta =\frac{3}{4}$, where $\theta$ is the angle of inclination of the line and $y-$ intercept is $\frac{-5}{3}$

Answer 1

Slope of the line is $m=\tan \theta =\frac{3}{4}$

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

$y=\frac{3}{4}x+\frac{-5}{3}$

$\Rightarrow 12y=9x-20$

$\therefore$equation of the line is $9x-12y-20=0$