The question is asking to find the rate of change (or slope) of the graph shown in the image. The line on the graph passes through several points, so we can calculate the slope using the formula for the rate of change between two points:

$\text{slope} = \frac{{\Delta y}}{{\Delta x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

Looking at the graph, we can see two points the line passes through:

• Point 1: $(0, -5)$
• Point 2: $(3, 2)$

Now, using the formula for the slope:

$\text{slope} = \frac{2 - (-5)}{3 - 0} = \frac{7}{3} \approx 2.33$

Since none of the options match exactly $2.33$, but $C. 2.5$ is the closest, we can choose Option C as the correct answer for the rate of change.

Would you like more details or have any questions?

Related Questions:

1. How do you determine the slope from a graph?
2. What does the rate of change tell you about the function's behavior?
3. What is the importance of identifying points clearly on a graph?
4. Can the rate of change be negative? Under what circumstances?
5. How can you apply the concept of slope in real-world situations?

Tip:

Always check two distinct points on the line and carefully calculate the rise and run to avoid mistakes when finding the slope.