To determine which relationship has a zero slope, we need to analyze the given data tables and calculate the slope for each.
### Table 1:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-3 & 2 \\
\hline
-1 & 2 \\
\hline
1 & 2 \\
\hline
3 & 2 \\
\hline
\end{array}
\][/tex]
### Table 2:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-3 & 3 \\
\hline
-1 & 1 \\
\hline
1 & -1 \\
\hline
3 & -3 \\
\hline
\end{array}
\][/tex]
#### Finding the Slope of Table 1:
- Slope is calculated as \(\frac{\Delta y}{\Delta x}\).
For Table 1:
- Between \((-3, 2)\) and \((-1, 2)\):
[tex]\[
\frac{2 - 2}{-1 - (-3)} = \frac{0}{2} = 0
\][/tex]
- Between \((-1, 2)\) and \( (1, 2)\):
[tex]\[
\frac{2 - 2}{1 - (-1)} = \frac{0}{2} = 0
\][/tex]
- Between \( (1, 2)\) and \( (3, 2)\):
[tex]\[
\frac{2 - 2}{3 - 1} = \frac{0}{2} = 0
\][/tex]
Since the slope is 0 for all intervals, the entire relationship in Table 1 has a zero slope.
#### Finding the Slope of Table 2:
For Table 2:
- Between \((-3, 3)\) and \((-1, 1)\):
[tex]\[
\frac{1 - 3}{-1 - (-3)} = \frac{-2}{2} = -1
\][/tex]
- Between \((-1, 1)\) and \( (1, -1)\):
[tex]\[
\frac{-1 - 1}{1 - (-1)} = \frac{-2}{2} = -1
\][/tex]
- Between \( (1, -1)\) and \( (3, -3)\):
[tex]\[
\frac{-3 - (-1)}{3 - 1} = \frac{-2}{2} = -1
\][/tex]
Since the slope is -1 for all intervals, the slope is not zero for Table 2.
### Conclusion:
The relationship in Table 1 has a zero slope.
