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Chapter 1: Problem 140

Explain why the slope of a vertical line is said to be undefined.

Short Answer

Expert verified
The slope of a vertical line is said to be undefined because the calculation of the slope involves division by zero, which is undefined in mathematics, due to the fact that there is no horizontal change in a vertical line.

Step by step solution

01

Define the slope of a line

The slope of a line is basically the 'steepness' of a line. It is defined as the change in y-values (vertical change) over the change in x-values (horizontal change), often represented as \( \Delta y / \Delta x \) or \( (y_{2} - y_{1}) / (x_{2} - x_{1}) \).
02

Discuss characteristics of vertical lines

For a vertical line, any two points that you take will have the same x-values (i.e., \( x_{2} = x_{1} \)). This means there is no horizontal change between any two points on a vertical line.
03

Relate to why slope of vertical line is undefined

So now if you try to find the slope of a vertical line, you have a situation where you're trying to divide by zero, since the change in x is zero. In mathematics, division by zero is undefined. Therefore, the slope of a vertical line is undefined.

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