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

$A=(-2,6)B=(3,-4)$

$P$ divides $AB$ in $2:3$ ratio

$x=\frac{m{x}_2+n{x}_1}{m+n}y=\frac{m{y}_2+n{y}_1}{m+n}$

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

$x=0y=2$

$P(0,2)m=\frac{3}{2}$

$(y-y_1)=m(x-x_1)$

$(y-2)=\frac{3}{2}(x-0)$

$2y-4=3x$

$3x-2y+4=0$.