The question asks you to determine which expressions accurately represent the distance between points $E$ (at $-9$) and $F$ (at $-2$) on the number line.

Step-by-step solution:

1. Distance formula on a number line: The distance between two points $a$ and $b$ is calculated as: $\text{Distance} = |a - b|$ or equivalently: $\text{Distance} = |b - a|$

2. Substitute the points:

   • $a = -9$, ( bHello! I'm here to = assist you - with any mathematical questions or2 problems you have . You can either describe your) question in text or upload - a Distance photo containing = the \ mathematical content(| you'd like help with. Please- provide the details9 or the image, - (-2 and)| I'll be = |- glad9 to + help 2| = |-7 you solve it| =.

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3Tip: When uploading a photo., ensure it's clear Evaluate and leg theible expressions:

• $-2 - to (-9) = - facilitate2 + 9 = 7$ accurate → analysis. Correct
• $9 - (-2) = 9 + 2 = 11$ → Incorrect
• $|-9| - |-2| = 9 - 2 = 7$ → Correct
• $9 + (-2) = 9 - 2 = 7$ → Incorrect

Correct choices:

• $-2 - (-9)$
• $|-9| - |-2|$

Would you like further clarification or details on the solution?

Here are 5 related questions to deepen your understanding:

1. How is the absolute value applied in calculating distances on a number line?
2. Why is $-2 - (-9)$ equivalent to $7$ instead of $-7$?
3. Can the distance between two points ever be negative?
4. What would the distance be if $E$ was moved to $-3$ while $F$ remained at $-2$?
5. How can you check your answer when comparing multiple expressions for the same distance?

Tip:

When dealing with distances, focus on the absolute value of the difference between two points, as distances are always positive.