Question

Find the equation of the line passing through $(3,5)$ and perpendicular to the line through the points $(2,5)$ and $(3,6)$.

Answer 1

The slope of line joining points $(2,5)$ and $(3,6)$ is $m=\frac{6-5}{-3-2}=\frac{1}{-5}$
We know that, the two non-vertical lines are perpendicular to each other only if and only if their slopes are negative reciprocals of each other.
Therefore, slope of line perpendicular to the line through the points $(2,3)$ and $(-3,6)$
$=-\frac{1}{m}=-\frac{1}{\left\{\frac{-1}{5}\right\}}=5$
Now equation of the line passing through points $(-3,5)$ whose slope is $5$ is $(y-5)=5(x+3)$.
$\Rightarrow y-5=5x+15$

$\Rightarrow 5x-y+20=0$