Context: The graph shows momentum $y$ (newton-seconds) against time $x$ (seconds), with points marked at $(0,1)$, $(2,2)$, $(4,4)$, $(6,8)$ and $(8,9)$. We need the average rate of change from $x = 2$ to $x = 6$.

Setup: Average rate of change is the slope of the straight line joining the two endpoints of the interval: $\text{average rate} = \frac{f(6) - f(2)}{6 - 2}$

Read the two values off the graph:

• At $x = 2$ the marked point is at $y = 2$, so $f(2) = 2$.
• At $x = 6$ the marked point is at $y = 8$, so $f(6) = 8$.

Solve: $\frac{8 - 2}{6 - 2} = \frac{6}{4} = 1.5$

Answer: $1.5$

Note that $3/2$ and $1.5$ are both ways to enter a correct answer.

Common slips:

• Reading $f(6)$ as $4$ by taking the marked point at $x = 4$ instead of $x = 6$. That gives $\dfrac{4-2}{4} = 0.5$, which is the most common wrong answer here — count the gridlines carefully.
• Using the endpoints of the whole graph, $(0,1)$ and $(8,9)$, which gives $1$ rather than the rate over the requested interval.
• Finding the slope at a single instant rather than the average across the interval. Average rate of change only needs the two endpoints; the shape of the curve between them does not matter.