https://file.aiquickdraw.com/mathbot/file/172926868348897lndr6w.jpg

To solve this, we need to analyze the graph and the options provided.

The graph shows two green dots at \(-12\) and \(-4\) on a number line, which indicates that these values are solutions of the absolute value equation.

The general form of an absolute value equation is:

\[
|x - a| = b
\]

Where \(a\) is the central point (midpoint between the two solutions) and \(b\) is the distance from \(a\) to one of the solutions.

1. **Find the midpoint:**
   - The two points are \(-12\) and \(-4\). 
   - The midpoint is \(\frac{-12 + (-4)}{2} = \frac{-16}{2} = -8\).

2. **Find the distance:**
   - The distance between \(-12\) and \(-8\) is \(4\), which is the value of \(b\).

Thus, the absolute value equation is:

\[
|x + 8| = 4
\]

The correct answer is the option **\(|x + 8| = 4\)**.

Would you like more details or have any questions?

### Related questions:
1. What are other examples of absolute value equations with different midpoints?
2. How do we determine the solutions to an absolute value equation like \(|x + 8| = 4\)?
3. What happens if the distance between the two points is greater than 4?
4. Can you explain the geometric meaning of an absolute value function on a number line?
5. How do we solve an absolute value equation when the absolute value is equal to zero?

### Tip:
Always remember that the absolute value represents the distance from a central point, so finding the midpoint is a key step to constructing the equation.

Which absolute value equation represents the graph shown?

Explore how to determine the absolute value equation that matches points on a number line. This problem involves finding the midpoint and distance of solutions to form the equation, ideal for Grades 6-8.

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