Question

Find the equation of the line which:
Passes through $(2,-1)$ and is perpendicular to $y=-\frac{1}{2}x+1$

Answer 1

Let slope of required line $=m_1$

Slope of $y=-\frac{1}{2}x+1$, $m_2=\frac{-1}{2}$ $\{y=mx+c\}$

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

$\Rightarrow m_1=2$

From point slope form, equation of line:

$y+1=2(x-2)$

$\Rightarrow y=2x-5$.