Question

The expression below represents the distance between two points on a number line.

|
−
5
−
4
|

Which number line shows the two points?

A.
The number line between -9 and 8 shows point a at -5 and point b at 4.

B.
The number line between -9 and 8 shows point a at -5 and point b at -4.

C.
The number line between -9 and 8 shows point a at -9 and point b at 4.

D.
The number line between -9 and 8 shows point a at 4 and point b at 5.

Answer 1

To determine which number line shows the two points represented by the expression \(|-5 - (-4)|\), we can first rewrite the expression:

\[
|-5 - (-4)| = |-5 + 4| = |-1| = 1
\]

This means that the distance between the two points (which we can denote as point \(a\) and point \(b\)) is equal to 1.

For the expression \(|a - b| = 1\), if we assume point \(a = -5\) and point \(b = -4\):

\[
|-5 - (-4)| = |-5 + 4| = |-1| = 1
\]

Now, let's go through the options to see which number line correctly represents this:

A. The number line shows point a at -5 and point b at 4.
- The distance is \(|-5 - 4| = |-9| = 9\), not 1.

B. The number line shows point a at -5 and point b at -4.
- The distance is \(|-5 - (-4)| = |-5 + 4| = |-1| = 1\), which is correct.

C. The number line shows point a at -9 and point b at 4.
- The distance is \(|-9 - 4| = |-13| = 13\), not 1.

D. The number line shows point a at 4 and point b at 5.
- The distance is \(|4 - 5| = |-1| = 1\), but it does not match our original points of -5 and -4.

The correct answer is **B**, since it represents the two points -5 and -4 properly with a distance of 1.