Using the chart, find the rate of change between the second and third points given as you look left to right:



To find the rate of change between the second and third points in the table as we move left to right, we need to use the coordinates for these points.

The given data points are:

- Second point: \((x_2, y_2) = (-5, 14)\)
- Third point: \((x_3, y_3) = (-3, 17)\)

The formula for the rate of change (slope) between two points \((x_2, y_2)\) and \((x_3, y_3)\) is:

\[
\text{Slope (m)} = \frac{y_3 - y_2}{x_3 - x_2}
\]

Substitute the given values into the formula:

\[
m = \frac{17 - 14}{-3 - (-5)}
\]

Simplify the expression:

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

So, the rate of change between the second and third 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 interpret the rate of change in the context of this table?
2. How does the rate of change between the second and third points compare to that between the first and second points?
3. What would the graph of these points look like if plotted on a coordinate plane?
4. If the rate of change remains constant, what does that indicate about the relationship between \(x\) and \(y\)?
5. How would the analysis change if the points did not follow a linear pattern?

**Tip:** Consistent rates of change between multiple pairs of points suggest a linear relationship.

Learn how to find the rate of change (slope) between two points (-5, 14) and (-3, 17) on a coordinate plane. Understand the concept of slope and its application in calculating rates of change. Suitable for Grades 7-9 students.

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