Answer
a. Rate of change = $\frac{3}{2}$
b. $f(x) = \frac{3}{2}x + 7$
Work Step by Step
a. The rate of change is how much $y$-increases for every increase in the $x$ value. Since when $x$ increases by $2$, $y$ increases by $3$, the rate of change is
$\text{Rate of change} = \dfrac{\text{Increase in }y}{\text{Increasi in }x}=\frac{3}{2}$.
b. The rate of change is $a$ and the $y$-intercept is $b$. The $y$-intercept occurs when $x = 0$, which means that, based on the chart given, $b= 7$.
So the overall equation for the function is
$f(x) = \frac{3}{2}x + 7$
