## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 2 - 2.1 - Linear Equations in Two Variables - 2.1 Exercises - Page 172: 104

#### Answer

A vertical line has an undefined slope because of the way the slope formula is written. The slope formula is: slope = $\frac{y_{final} - y_{initial}}{x_{final} - x_{initial}}$ A vertical line has the same x value for any y value, so between any two points on the line, the change in x will be zero. This means the slope would be: slope = $\frac{y_{final} - y_{initial}}{0}$ Since it is not mathematically possible to divide by 0, the slope is undefined.

#### Work Step by Step

A vertical line has an undefined slope because of the way the slope formula is written. The slope formula is: slope = $\frac{y_{final} - y_{initial}}{x_{final} - x_{initial}}$ A vertical line has the same x value for any y value, so between any two points on the line, the change in x will be zero. This means the slope would be: slope = $\frac{y_{final} - y_{initial}}{0}$ Since it is not mathematically possible to divide by 0, the slope is undefined.

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