Question

If points $(x_1,4),(-2,y_1)$ lie on the line joining the points $(2,-1)$ and $(5,-3),$ then the value of $2x_1+9y_1$ is

Answer 1

The equation of the line joining the points $(2,-1)$ and $(5,-3)$ is given by
$y+1=\frac{-1+3}{2-5}(x-2)\Rightarrow 2x+3y-1=0$

Since, $(x_1,4)$ and $(-2,y_1)$ lie on the line $2x+3y-1=0$, therefore
$2x_1+12-1=0\Rightarrow x_1=-\frac{11}{2}$
And $-4+3y_1-1=0$
$\Rightarrow y_1=\frac{5}{3}$

$\therefore 2x_1+9y_1=-11+15=4$