Answer
a) The rate of change is $1.5$
b) $f(x)=1.5x+7$.
Work Step by Step
a) The rate of change (slope) can be calculated from the first two points:
$\frac{f(y)-f(x)}{y-x}=\dfrac{f(2)-f(0)}{2-0}=\dfrac{10-7}{2-0}=\dfrac{3}{2}=1.5$
b) $f(x)=7$ at $x=0$, so the y-intercept is $b=7$. Hence, we have:
$f(x)=1.5x+7$.
