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