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 in the table as we look from left to right, we use the formula for the rate of change, which is essentially the slope between the two points.

### Given Table:

\[
\begin{array}{c|c|c|c|c|c}
x & -7 & -5 & -3 & -1 & 0 \\
\hline
y & 11 & 14 & 17 & 20 & 23 \\
\end{array}
\]

### Step 1: Identify the first two points:
- First point: \((-7, 11)\)
- Second point: \((-5, 14)\)

### Step 2: Apply the formula for the rate of change (slope):

\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the values:

\[
\text{Rate of change} = \frac{14 - 11}{-5 - (-7)} = \frac{3}{2} = 1.5
\]

### Conclusion:
The rate of change between the first two points \((-7, 11)\) and \((-5, 14)\) is **1.5**.

Would you like further details or have any questions?

Here are five related questions to consider:
1. How would the rate of change differ if you considered other pairs of points?
2. What does a consistent rate of change tell you about the relationship between \(x\) and \(y\)?
3. How can you use the rate of change to predict future values?
4. What is the significance of the rate of change in real-world applications

Learn how to calculate the rate of change between points -7 and -5 using the slope formula. This example uses a table of values to illustrate the concept of rate of change in mathematics. Suitable for Grades 7-9.

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