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.