Question

Find the equation of the straight line which pass through (4,3) and are respectively parallel and perpendicular to the x axis.

Answer 1

Dear student,

$$\begin{gathered} Weknowequationofx-axisisy=0. \\ Slopeofthislinem=0 \\ Nowslopeoflineparallel{m}_{1}tothex-axiswilbem=m_1 \\ \therefore Equationoflinewillbey-y_1=m_1\left(x-x_1\right) \\ \Rightarrow y-3=0\left(x-4\right) \\ \Rightarrow y-3=0 \\ \Rightarrow y=3 \\ Alinethatisperpendiculartothex-axisisaverticallikewithaslopeequaltoinfinity. \\ \therefore Equationoflinewillbey-y_1=m_1\left(x-x_1\right) \\ \Rightarrow y-3=\infty \left(x-4\right) \\ \Rightarrow \frac{y-3}{\infty }=\left(x-4\right) \\ \Rightarrow x-4=0 \\ \Rightarrow x=4 \end{gathered}$$
Regards