To determine which table represents the same relation as the given set of points [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex], we need to examine each table and compare its entries with the given set.
Let's look at each table individually.
### Table 1
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & -3 \\
\hline
4 & 2 \\
\hline
-4 & -1 \\
\hline
0 & 2 \\
\hline
\end{array}
\][/tex]
Looking at the pairs in this table:
[tex]\[
(-6, -3), (4, 2), (-4, -1), (0, 2)
\][/tex]
These pairs are not the same as any of the pairs in our given set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex].
### Table 2
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & 4 \\
\hline
-4 & 0 \\
\hline
-3 & 2 \\
\hline
-1 & 2 \\
\hline
\end{array}
\][/tex]
Looking at the pairs in this table:
[tex]\[
(-6, 4), (-4, 0), (-3, 2), (-1, 2)
\][/tex]
These pairs match exactly with the pairs in our given set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex].
### Table 3
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
6 & 4 \\
\hline
4 & 0 \\
\hline
3 & 2 \\
\hline
1 & 2 \\
\hline
\end{array}
\][/tex]
Looking at the pairs in this table:
[tex]\[
(6, 4), (4, 0), (3, 2), (1, 2)
\][/tex]
These pairs do not match the pairs in our given set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex].
Upon careful comparison, Table 2 is the one that matches the given set of points.
Therefore, the table that represents the same relation as the given set [tex]\(\{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\)[/tex] is:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & 4 \\
\hline
-4 & 0 \\
\hline
-3 & 2 \\
\hline
-1 & 2 \\
\hline
\end{array}
\][/tex]
So the correct answer is Table 2.
