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To find the average rate of change of the function \( g(x) = -1x + 3 \) between the points \((-2, 5)\) and \((1, 2)\), we can use the formula for the average rate of change between two points \((x_1, y_1)\) and \((x_2, y_2)\) on a function:

\[
\text{Average rate of change} = \frac{g(x_2) - g(x_1)}{x_2 - x_1}.
\]

Given the points:
- \( (x_1, y_1) = (-2, 5) \)
- \( (x_2, y_2) = (1, 2) \)

Substitute these into the formula:

\[
\text{Average rate of change} = \frac{2 - 5}{1 - (-2)} = \frac{2 - 5}{1 + 2} = \frac{-3}{3} = -1.
\]

So, the average rate of change of the function \( g(x) = -x + 3 \) between the points \((-2, 5)\) and \((1, 2)\) is \(-1\).

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

### 5 Related Questions:
1. What is the geometric interpretation of the average rate of change for a linear function?
2. How do you find the average rate of change for a non-linear function?
3. What does a negative average rate of change indicate about a function?
4. How would you find the instantaneous rate of change for the function \( g(x) = -x + 3 \) at a specific point?
5. If the function were non-linear, would the average rate of change still be constant between any two points?

### Tip:
For a linear function, the average rate of change between any two points is always equal to the slope of the line.

Find the average rate of change of g(x) = -1x + 3 between the points (-2, 5) and (1, 2).

Learn how to calculate the average rate of change for the linear function g(x) = -x + 3 between the points (-2, 5) and (1, 2). This tutorial provides a detailed step-by-step solution, ideal for students in Grades 9-12 studying algebra and linear functions.

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