Find the equation of the straight line which cuts off an intercept $3$ from the $Y$ axis and is inclined at an angle $\tan^{-1} \left(\dfrac{2}{3}\right)$ to the $X$ axis.
Intercept on the $Y$ axis $= c = 3$
Inclination of the required line to the $X$ axis $= \theta = \tan^{-1} \left(\dfrac{2}{3}\right)$
$\therefore \;$ Slope of the required line $= m = \tan \theta = \tan \left[\tan^{-1} \left(\dfrac{2}{3}\right)\right] = \dfrac{2}{3}$
The equation of the required line is of the form: $\;$ $y = mx + c$
i.e. $\;$ $y = \dfrac{2}{3} \times x + 3$
$\therefore \;$ The equation of the required line is: $\;$ $2x -3y + 9 = 0$