Let's solve for the rate of change of the graph on the interval \([-1, 4]\).

### Step-by-Step Solution

The **rate of change** between two points on a graph (or the slope of a line segment) is calculated using the formula:

\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

where:
- \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points on the graph.

### Identifying the Points

From the graph, let's find the coordinates at:
- \(x_1 = -1\)
- \(x_2 = 4\)

1. At \(x = -1\), the graph has a point \((-1, -2)\).
2. At \(x = 4\), the graph has a point \((4, 1)\).

### Calculate the Rate of Change

Now, apply the formula:

\[
\text{Rate of Change} = \frac{1 - (-2)}{4 - (-1)}
\]

Simplify the expression:

\[
\text{Rate of Change} = \frac{1 + 2}{4 + 1} = \frac{3}{5} = 0.6
\]

### Conclusion

The **rate of change** on the interval \([-1, 4]\) is **0.6**.

Would you like more details, or do you have any questions?

### Related Questions

1. How would you interpret the rate of change in different contexts, such as speed or growth rate?
2. What is the geometric significance of the rate of change in a linear function?
3. How does the rate of change differ when dealing with nonlinear functions?
4. What happens to the rate of change when the interval is modified?
5. How can you find the average rate of change over multiple intervals?

**Tip:** The rate of change represents how much one quantity changes, on average, relative to the change in another quantity over a specific interval. It can help in understanding trends and patterns in data.

Learn how to calculate the rate of change for a graph on the interval [-1, 4] with a detailed step-by-step solution. This problem covers key mathematical concepts including rate of change, slope calculation, and linear functions. Suitable for students in Grades 9-12.

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