Question

Find the equation of the line whose gradient is $\frac{3}{2}$ and which passes through $P$, where $P$ divides the line segment joining $A(-2,6)$ and $B(3,-4)$ in the ratio $2:3$ internally.

Answer 1

The coordinates of $P$ are $(\frac{l{x}_2+m{x}_1}{l+m}+\frac{l{y}_2+m{y}_1}{l+m})$
$=[\frac{2\left(3\right)+3(-2)}{2+3},\frac{2(-4)+3\left(6\right)}{2+3}]$
$=(\frac{6-6}{5},\frac{-8+18}{5})$
$=(0,2)$
Point $(0,2)$; Slope = $\frac{3}{2}$
The required equation is
$y-y_1=m(x-x_1)$
$\Rightarrow y-2=\frac{3}{2}(x-0)$
$\Rightarrow 2y-4=3x$
$\Rightarrow 3x-2y+4=0$