To complete the table for the equation [tex]\(-3x + 2y = -6\)[/tex], we will determine the corresponding [tex]\(y\)[/tex] values for given [tex]\(x\)[/tex] values. We need to find the [tex]\(y\)[/tex] values for [tex]\(x = -3\)[/tex], [tex]\(x = -1\)[/tex], and [tex]\(x = 0\)[/tex].
Here's how we do this step by step:
1. For [tex]\(x = -3\)[/tex]:
[tex]\[
-3(-3) + 2y = -6 \\
9 + 2y = -6 \\
2y = -6 - 9 \\
2y = -15 \\
y = \frac{-15}{2} \\
y = -7.5
\][/tex]
2. For [tex]\(x = -1\)[/tex]:
[tex]\[
-3(-1) + 2y = -6 \\
3 + 2y = -6 \\
2y = -6 - 3 \\
2y = -9 \\
y = \frac{-9}{2} \\
y = -4.5
\][/tex]
3. For [tex]\(x = 0\)[/tex]:
[tex]\[
-3(0) + 2y = -6 \\
0 + 2y = -6 \\
2y = -6 \\
y = \frac{-6}{2} \\
y = -3.0
\][/tex]
Now let's complete the table with the calculated values:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-3 & -7.5 \\
\hline
-1 & -4.5 \\
\hline
0 & -3.0 \\
\hline
\end{tabular}
So, the completed table is:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-3 & -7.5 \\
\hline
-1 & -4.5 \\
\hline
0 & -3 \\
\hline
\end{tabular}
