Question

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

Answer 1

Slope of the line $(2,5)$ and $(-3,6)$ is $\frac{6-5}{-3-2}=\frac{-1}{5}$

slope of the line perpendicular to the line passing through $(-3,5)$ is $=\frac{-1}{\frac{-1}{5}}=5$

Equation of the line passing through $(-3,5)$ is $y-5=5(x+3)$

$y-5=5x+15$

$\Rightarrow 5x-y+20=0$ is the required equation.