Explain why the slope of a vertical line is called undefined

The slope of a line is: "the change in y" over "the change in x" ;
or: "rise over run". A vertical line has NO "change in y" over "change in x" ; that is, has NO "rise over run"; so there is NO particular slope to mention or define. As such, the slope of a vertical line is "undefined".

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MrRoyal MrRoyal · Answer 2 · 2022-02-17T11:38:38+01:00

The slope is the change in the output value of a function, over the change in the input value

When the slope is undefined, then the line is a vertical line.

This is so because, there is no change in the input values of the function.

In other words, we have:

[tex]m = \frac{y_2 -y_1}{x_2 - x_1}\\[/tex]

Where:

[tex]x_1 = x_2[/tex]

Hence, the slope of a vertical line is called undefined because, there is no change in the input values of the function.