https://file.aiquickdraw.com/mathbot/file/17292689386197rvibxby.jpg

To interpret the graph and write the corresponding absolute value equation, let's analyze the information provided:

- The green dots on the number line are located at \(x = 4\) and \(x = 6\).
- The absolute value equation will be of the form \(|x - a| = b\), where \(a\) is the midpoint between the two values, and \(b\) is the distance from the midpoint to either endpoint.

### Step-by-step solution:

1. **Find the midpoint:**
   - The two points are 4 and 6.
   - Midpoint \(a = \frac{4 + 6}{2} = 5\).

2. **Find the distance from the midpoint to one of the points (this will be \(b\)):**
   - The distance between 5 and either endpoint (4 or 6) is 1.
   - So, \(b = 1\).

### The equation is:
\[
|x - 5| = 1
\]

This is the absolute value equation that represents the graph.

Let me know if you would like more details or have any questions!

Here are 5 related questions to deepen your understanding:

1. How do you calculate the midpoint of any two numbers on a number line?
2. Why is the absolute value equation centered at the midpoint?
3. What happens if the distance between the points is different? How does it affect \(b\)?
4. Can you write an absolute value equation for a graph with points at \(x = -2\) and \(x = 2\)?
5. How would you adjust the equation if one of the points were negative?

**Tip:** The variable \(b\) in an absolute value equation represents the distance between the number and its central value \(a\).

Write an absolute value equation that represents the graph shown with points at x = 4 and x = 6.

This problem involves finding the absolute value equation representing a number line with points at x = 4 and x = 6. Learn how to apply the midpoint formula and absolute value properties to solve this problem, suitable for Grades 7-9.

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