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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 formula for calculating slope results in a division by zero in this case, which is undefined in mathematics.

Step by step solution

01

Understanding The Concept of Slope

The slope of a line in a two-dimensional space is a measure of how steep the line is. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. For any two points \((x_1, y_1)\) and \((x_2, y_2)\) on a line, the slope m is calculated as: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
02

Slope of a Vertical Line

A vertical line goes straight up and down, so any two points on the line have the same x value. This means the horizontal change, or run, between any two points on a vertical line is zero. If we plug this into our formula for slope, we get: \(m = \frac{y_2 - y_1}{0}\)
03

Undefined Slope

Division by zero is undefined in mathematics. Therefore, the slope of a vertical line, which involves division by zero, is also undefined.

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