# Chapter 2, Functions - Section 2.4 - Average Rate of Change of a Function - 2.4 Exercises - Page 224: 26

(a) -4 (b) the slope is also -4

#### Work Step by Step

(a) We find the average rate of change from $x=a$ to $x=a+h$: $\frac{g(a+h)-g(a)}{(a+h)-a}=\frac{[-4(a+h)+2]-[-4a+2]}{h}=\frac{-4a-4h+2+4a-2}{h}=\frac{-4h}{h}=-4$ (b) A line has the form $f(x)=mx+b$, with $m=slope$. For the line $g(x)=-4x+2$, the slope is $\displaystyle -4$, which equals what we got in (a).

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