Question

Find the equation of straight lines which passes through $(2,1)$ and are respectively parallel and perpendicular to the $x-axis$.

Answer 1

Let equation of line

$y=mx+c\to \left(i\right)$

$\Rightarrow$ if line parallel to x-axis, then slope is zero (o)

$\therefore m=0$

put (2,1) in equation (i)

$\begin{array}{c}\Rightarrow 1=2m+c\\ \Rightarrow 1=0+c\\ c=1\end{array}$

Then equation of line

$\begin{array}{c}\Rightarrow y=mx+1\\ \Rightarrow y=0+1\\ y=1\end{array}$

if line $\perp r$ to x-axis, y=0.