A 3-column table with 4 rows. Column 1 is labeled a with entries 1, negative 1, negative 4, negative 6. Column 2 is labeled b with entries 2, negative 2, 1, negative 3. Column 3 is labeled Distance with entries 1 unit, X, Y, Z. A number line going from negative 7 to positive 3.

Question

Distance is the number of units between two integers. Use number line to find the distance between each pair of integers.

X =
Y =
Z =

Answer 1

To find the distances represented by \(X\), \(Y\), and \(Z\), we will calculate the absolute differences between the integer pairs in columns \(a\) and \(b\):

1. For \(X\): The pair of integers is \(1\) (from column \(a\)) and \(2\) (from column \(b\)). \[ X = |1 - 2| = | -1 | = 1 \text{ unit} \]

2. For \(Y\): The pair of integers is \(-1\) (from column \(a\)) and \(-2\) (from column \(b\)). \[ Y = |-1 - (-2)| = |-1 + 2| = |1| = 1 \text{ unit} \]

3. For \(Z\): The pair of integers is \(-4\) (from column \(a\)) and \(-3\) (from column \(b\)). \[ Z = |-4 - (-3)| = |-4 + 3| = |-1| = 1 \text{ unit} \]

Now, compiling our results:

• \(X = 1\)
• \(Y = 1\)
• \(Z = 1\)

Thus, we can conclude:

• \(X = 1\)
• \(Y = 1\)
• \(Z = 1\)