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 $x-$intercept is $5$

Answer 1

$x-$intercept is $5$

Using slope intercept form, the equation of the line is $y=m(x-d)$

$y=\frac{2}{3}(x-5)$

$\Rightarrow 3y=2x-15$

$\therefore$ equation of the line is $2x-3y-15=0$