Answer
a) The rate of change is $0.5$
b) $f(x)=0.5x-1$.
Work Step by Step
a: The rate of change (slope) can be calculated from two points:
$\frac{f(y)-f(x)}{y-x}=\frac{f(4)-f(2)}{4-2}=\frac{1-0}{4-2}=\frac{1}{2}=0.5=a$.
b) $f(x)=-1$ at $x=0$, so the y-intercept is $b=-1$. Hence, we have: $f(x)=0.5x-1$.
