Chapter 8.4, Problem 17HP

To determine

To explain:why a vertical line cannot be used to represent a rate of change.

Answer to Problem 17HP

The vertical line states that as y increases the value of x remains constant. So, the rate of change for vertical lines is not defined.

Explanation of Solution

Calculation:

The rate of change is change in one quantity with respect to another quantity.

Mathematically:

  $Rateofchange=\frac{change\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}iny}{changeinx}$

The horizontal line states that as x increases, the value of y remains constant. So, the rate of change for horizontal line is 0.

The vertical line states that as y increases, the value of x remains constant. So, the rate of change for vertical line is not defined.

Conclusion:

Therefore, the vertical lines cannot be used to represent a rate of change.