https://file.aiquickdraw.com/mathbot/file/1729268821334zq5abc2q.jpg

To solve the given problem, we need to match the absolute value equation with the number line graph shown.

### Step-by-Step Analysis:
1. **Key points on the number line:**
   The graph shows two green points at \( x = 1 \) and \( x = 6 \). These are the points that determine the solution set of the absolute value equation.

2. **Structure of absolute value equations:**
   Absolute value equations take the form:
   \[
   |x - c| = d
   \]
   where:
   - \( c \) is the midpoint between the two points on the number line,
   - \( d \) is the distance from the midpoint \( c \) to either endpoint (green dots).

3. **Finding the midpoint:**
   The midpoint between \( 1 \) and \( 6 \) is calculated as:
   \[
   c = \frac{1 + 6}{2} = 3.5
   \]

4. **Finding the distance:**
   The distance from the midpoint \( 3.5 \) to either point (1 or 6) is:
   \[
   d = 6 - 3.5 = 2.5
   \]

### Conclusion:
The absolute value equation that represents the graph is:
\[
|x - 3.5| = 2.5
\]

Thus, the correct choice is the first option: **\( |x - 3.5| = 2.5 \)**.

Let me know if you want further details or have any questions!

Here are 5 related questions you might want to explore:
1. How do you solve absolute value equations algebraically?
2. What is the geometric interpretation of absolute value functions on the number line?
3. How do we find the midpoint between two numbers?
4. What are the different forms of absolute value equations?
5. How does shifting an absolute value function horizontally affect its graph?

**Tip:** When solving an absolute value equation like \( |x - c| = d \), the solutions are \( x = c - d \) and \( x = c + d \), giving you two points on the number line.

Which absolute value equation represents the graph shown?

Learn how to find the absolute value equation |x - 3.5| = 2.5 by analyzing the number line with points at x = 1 and x = 6. This solution involves the midpoint formula and the properties of absolute value equations, making it ideal for students in Grades 7-10.

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