Answer
a. $\frac{1}{2}$, $\frac{1}{2}$
b. The average rate of change is the same.
c. $m=\frac{1}{2}$
Work Step by Step
$f(x)=\frac{1}{2}x-6$,
a.
at $x=0, f(0)=-6$ and at $x=2, f(2)=-5$,
thus, the Average rate of change is $\frac{f(2)-f(0)}{2-0}=\frac{1}{2}$.
at $x=15, f(15)=\frac{3}{2}$ and at $x=50, f(50)=19$.
thus, the Average rate of change is $\frac{f(50)-f(15)}{50-15}=\frac{1}{2}$.
b.
from (a) we can see that An Average rate of change is the same.
c.
Since $f(x)$ is a function is a degree one function, The function is linear.
and from the linear function of the form $y=mx+b$, we can get an average rate of change $m$. thus, in this case $f(x)=\frac{1}{2}x-6$, we can get an average rate of change to be $m=\frac{1}{2}$
