# To calculate the average rate of change to show that it is the same as the slope m ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.4, Problem 32E
To determine

## To calculate the average rate of change to show that it is the same as the slope m

Expert Solution

The average rate of change to show that it is the same as the slope m

### Explanation of Solution

Given information:

f(x)=mx+b is a linear function, and the average rate of change of f between any two real number x1 and x2 is f(x2)f(x1)x2x1

Calculation:

f(x2)f(x1)x2x1=mx2+b(mx1+b)x2x1=m(x2x1)x2x1                       [divide out common factor]=m

Because f(x)=mx+b .

Hence, the average rate of change to show that it is the same as the slope m

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