Find the equation of a line whose slope is $\dfrac{3}{2}$ and passes through the point $P$ which divides the line segment joining $A \left(-2, 6\right)$ and $B \left(3, -4\right)$ in the ratio $2 : 3$.
Point $P \left(x,y\right)$ divides the line segment $A \left(-2, 6\right)$ and $B \left(3, -4\right)$ in the ratio $2 : 3$.
$\therefore \;$ By section formula
$x = \dfrac{2 \times 3 + 3 \times \left(-2\right)}{2 + 3} = 0$; $\;\;\;$ $y = \dfrac{2 \times \left(-4\right) + 3 \times 6}{2 + 3} = 2$
$\therefore \;$ $P \left(x, y\right) = P \left(0, 2\right)$
Equation of line passing through the point $P$ and slope $= \dfrac{3}{2}$ is
$y - 2 = \dfrac{3}{2} \left(x - 0\right)$
i.e. $\;$ $3x - 2y + 4 = 0$