g(x)=1x+3 find the rate of change between (-1, 2) and (2,5)

To find the rate of change (also known as the slope) between two points on a function, we use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Given the points \((-1, 2)\) and \((2, 5)\):

1. \(x_1 = -1\), \(y_1 = 2\)
2. \(x_2 = 2\), \(y_2 = 5\)

Substitute these values into the slope formula:

\[
\text{slope} = \frac{5 - 2}{2 - (-1)} = \frac{3}{2 + 1} = \frac{3}{3} = 1
\]

So, the rate of change between the points \((-1, 2)\) and \((2, 5)\) is \(1\).

Would you like a more detailed explanation or have any questions?

Here are 5 questions to expand your understanding:
1. How do we interpret the rate of change in a linear function?
2. What does the rate of change tell us about the graph of a function?
3. How can you find the slope of a nonlinear function between two points?
4. If the slope is 0, what does that indicate about the function between two points?
5. How would the rate of change differ if we used a quadratic function?

**Tip:** The slope of a linear function is constant between any two points, meaning the rate of change is always the same for linear functions.

g(x) = 1/(x+3), find the rate of change between (-1, 2) and (2, 5).

Learn how to calculate the rate of change for the function g(x) = 1/(x+3) between the points (-1, 2) and (2, 5) using the slope formula. This problem covers key algebra concepts such as rate of change and slope. Suitable for students in Grades 8-10.

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