Question

What is the slope of a line parallel to the $y$-axis?

Answer 1

Determine the slope of a line parallel to the $y$-axis.

The slope of a line is $m=\tan \left(\theta \right)$, where $\theta$ is the angle made by the line with the $x$-axis.

We know that, $\theta =\frac{\mathrm{\pi }}{2}$ when a line parallel to $y$-axis.

So, the required slope is:

$\begin{array}{rcl}m& =& \tan \left(\frac{\mathrm{\pi }}{2}\right)\\ & \Rightarrow & m=\infty \left[\because \tan \left(\frac{\mathrm{\pi }}{2}\right)=\infty \right]\\ \therefore m& =& \infty \end{array}$

Hence, the required solution is undefined.