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

Given, P divides the line segment joining A (-2, 6) and B (3, -4) in the ratio 2: 3.

Co-ordinates of point P are $(\frac{(2\times 3)+(3\times -2)}{2+3},\frac{(2\times -4)+(3\times 6)}{2+3})$
$=(\frac{6-6}{5},\frac{-8+18}{5})$
$=(\frac{0}{5},\frac{10}{5})$
$=(0,2)=P(x_1,y_1)$

Slope of the required line = $m=\frac{3}{2}$

The required equation of the line is given by

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

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

$\Rightarrow 2y-4=3x$

$\therefore 2y=3x+4$ is the required equation of line.