I'm having trouble with b. any suggestions on how to get started without having the equation for f'(x) ?
You don't need it.
Your graph shows the derivative of $\displaystyle f$, or the slope of $\displaystyle f$ at every point on the closed interval [-3, 7]
Your graph shows that at $\displaystyle x=2$, $\displaystyle f'(x)=1$, or that the slope at $\displaystyle x=2$ is 1.
You also know that the function takes on the value $\displaystyle f(2)=3$
Plug these two known facts into the equation $\displaystyle y=mx+b$, find the intercept $\displaystyle b$ and you're done.