Sure, let's analyze the relationship described by [tex]\( y = 2x - 5 \)[/tex] and complete the table step-by-step.
We will evaluate the expression [tex]\( y = 2x - 5 \)[/tex] for each given [tex]\( x \)[/tex] value.
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 2(-2) - 5
\][/tex]
[tex]\[
y = -4 - 5 = -9
\][/tex]
The pair [tex]\((x, y)\)[/tex] is [tex]\((-2, -9)\)[/tex].
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 2(-1) - 5
\][/tex]
[tex]\[
y = -2 - 5 = -7
\][/tex]
The pair [tex]\((x, y)\)[/tex] is [tex]\((-1, -7)\)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 2(0) - 5
\][/tex]
[tex]\[
y = 0 - 5 = -5
\][/tex]
The pair [tex]\((x, y)\)[/tex] is [tex]\((0, -5)\)[/tex].
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 2(1) - 5
\][/tex]
[tex]\[
y = 2 - 5 = -3
\][/tex]
The pair [tex]\((x, y)\)[/tex] is [tex]\((1, -3)\)[/tex].
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2(2) - 5
\][/tex]
[tex]\[
y = 4 - 5 = -1
\][/tex]
The pair [tex]\((x, y)\)[/tex] is [tex]\((2, -1)\)[/tex].
Now we can fill in the table with our calculated values:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
x & y & (x, y) \\
\hline
-2 & -9 & (-2, -9) \\
\hline
-1 & -7 & (-1, -7) \\
\hline
0 & -5 & (0, -5) \\
\hline
1 & -3 & (1, -3) \\
\hline
2 & -1 & (2, -1) \\
\hline
\end{tabular}
\][/tex]
So, the completed table is:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
x & y & (x, y) \\
\hline
-2 & -9 & (-2, -9) \\
\hline
-1 & -7 & (-1, -7) \\
\hline
0 & -5 & (0, -5) \\
\hline
1 & -3 & (1, -3) \\
\hline
2 & -1 & (2, -1) \\
\hline
\end{tabular}
\][/tex]
