Question

What is the slope of a line perpendicular to the $x-$axis?

Answer 1

To find the slope of the line:

The slope of the $x-$axis is zero.

Since the slope of the perpendicular line is $-\frac{1}{\text{slope of the given line}}$, so the slope of the perpendicular line is calculated in below:

$\begin{array}{rcl}m& =& -\frac{1}{0}\\ & =& \text{undefined}\end{array}$

Hence, the slope of a line perpendicular to the $x-$axis is undefined.