https://file.aiquickdraw.com/mathbot/file/17276615808268np5ywng.jpg

Let's analyze the number line in the image and answer the questions based on the points provided:

1. **Identifying the points**:  
   The two points on the number line are marked at **-2** and **4**.

2. **Midpoint formula**:  
   The formula for the midpoint between two points \( x_1 \) and \( x_2 \) on a number line is:  
   \[
   \text{Midpoint} = \frac{x_1 + x_2}{2}
   \]
   Substituting the values:
   \[
   \text{Midpoint} = \frac{-2 + 4}{2} = \frac{2}{2} = 1
   \]
   So, the **midpoint** is **1**.

3. **Distance between either point and the midpoint**:  
   The distance formula between two points on a number line is the absolute difference:  
   \[
   \text{Distance} = |x_1 - x_2|
   \]
   The distance between -2 and the midpoint (1) is:
   \[
   |1 - (-2)| = |1 + 2| = 3
   \]
   The distance between 4 and the midpoint (1) is:
   \[
   |4 - 1| = 3
   \]
   So, the **distance** between either point and the midpoint is **3**.

4. **Absolute value equation**:  
   The general form of an absolute value equation representing the distance from a point \( x \) to a center is:
   \[
   |x - \text{Midpoint}| = \text{Distance}
   \]
   Here, the midpoint is 1, and the distance is 3. Thus, the equation becomes:
   \[
   |x - 1| = 3
   \]

### Answers:
- The midpoint between the two points is **1**.
- The distance between either point and the midpoint is **3**.
- The absolute value equation for the graph is **|x - 1| = 3**.

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Would you like more details on any of these calculations?

Here are 5 related questions to deepen your understanding:
1. How do you calculate the distance between any two points on a number line?
2. What would the midpoint be if the points were -3 and 5?
3. How does the absolute value equation represent distances on a number line?
4. If one point is shifted further on the number line, how would the equation change?
5. How can the midpoint formula be extended to two-dimensional points?

**Tip**: The midpoint is always the average of the two numbers, and it's exactly halfway between them.

Enter your answers in the spaces provided: The midpoint between the two points shown on the number line is __. The distance between either point plotted on the number line and the midpoint is __. An absolute value equation for the graph is |x - __| = __.

Learn how to calculate the midpoint between two points on a number line and find the absolute value equation representing the graph. This problem explores key concepts such as distance, midpoint, and absolute value equations, suitable for Grades 6-8.

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