https://file.aiquickdraw.com/mathbot/file/1727213480056hmac1198.jpg

The graph shows two points: \(-14\) and \(-6\). To write the absolute value equation, we need to follow the form \(|x - a| = b\), where \(a\) is the midpoint between the two values, and \(b\) is the distance from \(a\) to either point.

1. **Find the midpoint** \(a\):
   \[
   a = \frac{-14 + (-6)}{2} = \frac{-20}{2} = -10
   \]

2. **Find the distance** \(b\) (the distance from the midpoint to either endpoint):
   \[
   b = |-10 - (-14)| = |-10 + 14| = 4
   \]

Thus, the absolute value equation representing the graph is:
\[
|x + 10| = 4
\]

Would you like more details on how this was derived, or have any questions?

Here are 5 relative questions to expand on the concept:
1. How do you find the distance between two points on a number line?
2. What are the steps to solve an absolute value equation like \(|x + 10| = 4\)?
3. How would the equation change if the points were shifted?
4. Can absolute value equations have no solution? Under what conditions?
5. How would you write an absolute value inequality for this graph?

**Tip:** Remember that the absolute value \(|x - a|\) represents the distance between \(x\) and \(a\) on the number line.

Write an absolute value equation that represents the graph shown with points at -14 and -6.

Learn how to write the absolute value equation for the points at -14 and -6 on a number line. This problem involves finding the midpoint and the distance, and translating them into an absolute value equation. Suitable for Grades 7-9.

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