To present a detailed, step-by-step solution, let's take a look at the given data in the table format and understand what it represents. We have two lists of data points for the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
Here's the given data:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 2 \\
\hline
7 & 0 \\
\hline
-4 & -4 \\
\hline
0 & -6 \\
\hline
\end{array}
\][/tex]
From the table, we can see the following pairs of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:
1. [tex]\( x = -4 \)[/tex], [tex]\( y = 2 \)[/tex]
2. [tex]\( x = 7 \)[/tex], [tex]\( y = 0 \)[/tex]
3. [tex]\( x = -4 \)[/tex], [tex]\( y = -4 \)[/tex]
4. [tex]\( x = 0 \)[/tex], [tex]\( y = -6 \)[/tex]
Now let's list out these pairs:
1. The first pair is [tex]\((-4, 2)\)[/tex].
2. The second pair is [tex]\((7, 0)\)[/tex].
3. The third pair is [tex]\((-4, -4)\)[/tex].
4. The fourth pair is [tex]\((0, -6)\)[/tex].
We can construct the lists for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values based on these pairs:
1. The [tex]\( x \)[/tex]-values (from the first column) are: [tex]\([-4, 7, -4, 0]\)[/tex].
2. The [tex]\( y \)[/tex]-values (from the second column) are: [tex]\([2, 0, -4, -6]\)[/tex].
Therefore, the lists derived from the given data are:
- List [tex]\( x \)[/tex] containing the values [tex]\([-4, 7, -4, 0]\)[/tex].
- List [tex]\( y \)[/tex] containing the values [tex]\([2, 0, -4, -6]\)[/tex].
These lists correspond to the values in the table, pair by pair, as recorded in the rows. The solution aligns with the given data, thus validating the values.
In summary, the final answer is:
[tex]\[
(\text{list of } x \text{ values}, \text{list of } y \text{ values}) = ([-4, 7, -4, 0], [2, 0, -4, -6])
\][/tex]
