Question

Write down 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 $2:3$.

Answer 1

R.E.F image

$P(0,2)x=\frac{2\left(3\right)+3(-2)}{2+3}=0$

$y=\frac{2(-4)+3\left(6\right)}{2+3}=2$

Line : $\frac{3}{2}=\frac{y-2}{x}\Rightarrow 3x=2y-4$