Let's solve the given equation [tex]\( x + 12 = 6y \)[/tex] for the provided [tex]\( x \)[/tex] values step-by-step.
### Step-by-Step Solution
1. Rewrite the equation to solve for [tex]\( y \)[/tex]:
The given equation is:
[tex]\[
x + 12 = 6y
\][/tex]
To solve for [tex]\( y \)[/tex], we isolate [tex]\( y \)[/tex] on one side of the equation:
[tex]\[
y = \frac{x + 12}{6}
\][/tex]
2. Calculate the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex] value:
- For [tex]\( x = -12 \)[/tex]:
[tex]\[
y = \frac{-12 + 12}{6} = \frac{0}{6} = 0.0
\][/tex]
- For [tex]\( x = -6 \)[/tex]:
[tex]\[
y = \frac{-6 + 12}{6} = \frac{6}{6} = 1.0
\][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = \frac{0 + 12}{6} = \frac{12}{6} = 2.0
\][/tex]
- For [tex]\( x = 6 \)[/tex]:
[tex]\[
y = \frac{6 + 12}{6} = \frac{18}{6} = 3.0
\][/tex]
- For [tex]\( x = 12 \)[/tex]:
[tex]\[
y = \frac{12 + 12}{6} = \frac{24}{6} = 4.0
\][/tex]
3. Fill in the table with the calculated [tex]\( y \)[/tex] values:
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$x$ & -12 & -6 & 0 & 6 & 12 \\
\hline
$y$ & 0.0 & 1.0 & 2.0 & 3.0 & 4.0 \\
\hline
\end{tabular}
\][/tex]
Thus, the table is completed with the values:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -12 & -6 & 0 & 6 & 12 \\
\hline
y & 0.0 & 1.0 & 2.0 & 3.0 & 4.0 \\
\hline
\end{array}
\][/tex]
