Question

Find the equations of the straight passing through $(1,3)$ and (i) parallel (ii) perpendicular to the line passing through the points $(3,-5)$ and $(-6,1)$

Answer 1

Line passing through $(3,-5)$ & $(-6,1)$ slope

$m=\frac{1+5}{-6+3}=\frac{6}{-9}=\frac{-2}{3}$

$i)$ Line parallel passing through $(1,3)$

$y-3=\frac{-2}{3}(x-1)$

$3y-9=-2x+2$

$3y+2x-11=0$

$ii)$ Line passing through $(1,3)$

$y-3=\frac{3}{2}(x-1)$

$2y-6=3x-3$

$2y-3x-3=0$