To solve for the average rate of change of the graph, we need to calculate the slope $m$, which is the "rate of change" between two points on the line. The slope formula is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Step 1: Identify two points from the graph.

From the image:

• One point on the line is $(0, 3)$.
• Another point is $(6, -3)$.

Step 2: Apply the slope formula.

Using the points $(0, 3)$ and $(6, -3)$:

$m = \frac{-3 - 3}{6 - 0} = \frac{-6}{6} = -1$

Conclusion:

The average rate of change (slope) of the graph is $m = -1$.

Would you like further details on the solution, or do you have any questions?

Here are 5 related questions to explore:

1. What does the slope of a line represent in real-world scenarios?
2. How would the graph change if the slope were positive instead of negative?
3. What are the units of the average rate of change in applied contexts like speed or growth?
4. How can you determine if two lines are parallel or perpendicular by comparing their slopes?
5. What would be the equation of the line given the slope and one point?

Tip: The slope indicates how steep a line is; a negative slope means the line is decreasing as you move from left to right.