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Using the chart below, find the rate of change between the first two point given as you look left to right:



To find the rate of change between the first two points as we look left to right in the table, we need to calculate the slope of the line passing through these two points. 

The table provides the following data points:

- First point: \( (x_1, y_1) = (-7, 11) \)
- Second point: \( (x_2, y_2) = (-5, 14) \)

The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
\text{Slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given values into the formula:

\[
m = \frac{14 - 11}{-5 - (-7)}
\]

Simplify the expression:

\[
m = \frac{3}{2} = 1.5
\]

So, the rate of change between the first two points is **1.5**.

Would you like further details or have any questions? Here are some related questions you might consider:

1. How do you calculate the rate of change for other pairs of points in the table?
2. What does the rate of change represent in a real-world context?
3. How would the rate of change be affected if the data points formed a curve instead of a straight line?
4. How can we determine if the rate of change is constant for all points in the table?
5. What other methods could be used to analyze the data presented in the table?

**Tip:** The rate of change (slope) is a measure of how much \(y\) changes for a unit change in \(x\). It is an essential concept in understanding linear relationships.

Learn how to find the rate of change between two points in a table using the slope formula. This problem involves calculating the slope between points (-7, 11) and (-5, 14), explaining the concept of rate of change and its application in linear equations. Suitable for Grades 7-9 students.

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