Question

Find the equation of the line which passes through $(-1,0)$ and is perpendicular to the line through $(3,1)$ and $(5,7)$.

Answer 1

Let slope of required line $=m_1$

Slope of line passing $(3,1)$ and $(5,7)$, $m_2=\frac{7-1}{5-3}=\frac{6}{2}=3$

Given, they are perpendicular $\Rightarrow m_1{m}_2=-1\Rightarrow m_1=\frac{-1}{3}$

From point slope form, $y-0=-\frac{1}{3}(x+1)$

$\Rightarrow 3y=-x-1$.