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.