Answer
a. 0.5
b. Yes, they are the same
c. Function is linear, rate of change = 0.5
Work Step by Step
$f(x) = 0.5x - 6$
a. Average Rate of change between x=0 and x=2, x=15 and x=50
Average Rate of Change (from x=0 to x=2): $\frac{f(2) - f(0)}{2-0} = \frac{-5 - (-6)}{2} = 0.5$
Average Rate of Change (from x=15 to x=50): $\frac{f(50) - f(15)}{50-15} = \frac{19 - (1.5)}{35} = 0.5$
b. Yes they are the same
c. The function is linear as it is in the form of $y=mx+ b$
The rate of change is 0.5 (given from a)
