Question

Which expressions represent the distance between the numbers on the number line? Select all that apply.

A number line from negative 6 to 8. There is a dot halfway between negative 4 and negative 2, and a dot at 2 with a line connecting the dots.

Answer 1

To determine the distance between two numbers on a number line, we typically use the formula:

\[
\text{Distance} = |a - b|
\]

where \(a\) and \(b\) are the two numbers.

For the points mentioned in your scenario:

1. **Negative 4 and Negative 2**:
- Using the distance formula, we calculate:
\[
\text{Distance} = |-4 - (-2)| = |-4 + 2| = |-2| = 2
\]

2. **Negative 4 and 2**:
- Using the distance formula again:
\[
\text{Distance} = |-4 - 2| = |-6| = 6
\]

3. **Negative 2 and 2**:
- For these two points:
\[
\text{Distance} = |-2 - 2| = |-4| = 4
\]

Based on these calculations, the expressions that represent the distance between the numbers on the number line are:

- \(|-4 - (-2)|\) which equals 2.
- \(|-4 - 2|\) which equals 6.
- \(|-2 - 2|\) which equals 4.

Thus, the correct expressions for the distances are \(|-4 - (-2)|\), \(|-4 - 2|\), and \(|-2 - 2|\). If any additional combinations of other numbers on the number line are included in your question, please specify, and I can help you further.