To determine which table of ordered pairs represents the equation [tex]\( 3x - 2y = 12 \)[/tex], we'll check which set of (x, y) pairs satisfies this equation.
Given the tables:
1.
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & -1 & 1 & 3 & 5 \\
\hline
$y$ & -7.5 & -4.5 & -1.5 & 1.5 \\
\hline
\end{tabular}
\][/tex]
2.
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & -7.5 & 4.5 & 1.5 & -1.5 \\
\hline
$y$ & 1 & 1 & 3 & 5 \\
\hline
\end{tabular}
\][/tex]
3.
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & -1 & 1 & 3 & 5 \\
\hline
$y$ & 7.5 & 4.5 & 1.5 & 1.5 \\
\hline
\end{tabular}
\][/tex]
4.
[tex]\[
\begin{tabular}[c]{|c|c|c|c|c|}
\hline
$x$ & -7.5 & -4.5 & -1.5 & 1.5 \\
\hline
\end{tabular}
\][/tex]
Let's check the pairs from each table:
Table 1:
- For [tex]\( x = -1, y = -7.5 \)[/tex]:
[tex]\[
3(-1) - 2(-7.5) = -3 + 15 = 12 \text{ (True)}
\][/tex]
- For [tex]\( x = 1, y = -4.5 \)[/tex]:
[tex]\[
3(1) - 2(-4.5) = 3 + 9 = 12 \text{ (True)}
\][/tex]
- For [tex]\( x = 3, y = -1.5 \)[/tex]:
[tex]\[
3(3) - 2(-1.5) = 9 + 3 = 12 \text{ (True)}
\][/tex]
- For [tex]\( x = 5, y = 1.5 \)[/tex]:
[tex]\[
3(5) - 2(1.5) = 15 - 3 = 12 \text{ (True)}
\][/tex]
Since all pairs from the first table satisfy the equation [tex]\( 3x - 2y = 12 \)[/tex], this is the correct table.
Table 1 correctly represents the equation:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & -1 & 1 & 3 & 5 \\
\hline
$y$ & -7.5 & -4.5 & -1.5 & 1.5 \\
\hline
\end{tabular}
\][/tex]
