Question

The slope of any line which is perpendicular to the $x$-axis is .......... .

• A. $0$
• B. $1$
• C. $-1$
• D. Not defined

Answer 1

The correct option is D Not defined

A horizontal line has slope $0$, because even though the value of $x$ changes, the value of $y$ does not change i.e. $\Delta y=0$.

$\frac{\Delta y}{\Delta x}=\frac{0}{\Delta x}=0$

Therefore, the slope of the $x$-axis is $0$.

Now since the slope of the perpendicular line is the negative reciprocal to the slope of the $x$-axis.

Therefore, the slope of the line is:

$\frac{1}{0}=$ undefined

Hence, the slope of the line perpendicular to the $x$-axis is not defined.