Answer
a. $\frac{1}{2}$
b. $\frac{1}{2}$=$\frac{1}{2}$
Work Step by Step
1. Simplify your two functions:
f(a)=$\frac{1}{2}$a+3
=$\frac{a}{2}$+3
f(a+h)=$\frac{1}{2}$(a+h)+3
=$\frac{a}{2}$+$\frac{h}{2}$+3
2. Find the difference between the two functions.
$\frac{a}{2}$+$\frac{h}{2}$+3-($\frac{a}{2}$+3)
=$\frac{a}{2}$+$\frac{h}{2}$+3-$\frac{a}{2}$-3
=$\frac{h}{2}$
3. Divide $\frac{h}{2}$ by (a+h-a) to find the average rate of change.
(a+h-a) simplifies to h
$\frac{h}{2}$$\div$h=$\frac{h}{2}$$\div$$\frac{h}{1}$
=$\frac{h}{2}$$\times$$\frac{1}{h}$
=$\frac{h}{2h}$
=$\frac{1}{2}$
For Part B, look at the original function:
f(x)=$\frac{1}{2}$x+3
It's already in y-intercept form, which allows you to see the slope just by looking at the function. The slope is $\frac{1}{2}$.
$\frac{1}{2}$=$\frac{1}{2}$.
