Let's construct the table for the given equation [tex]\( y = \frac{1}{4}x + 2 \)[/tex].
We'll calculate the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex] value: -4, 0, and 4.
1. For [tex]\( x = -4 \)[/tex]:
[tex]\[
y = \frac{1}{4}(-4) + 2
\][/tex]
[tex]\[
y = -1 + 2
\][/tex]
[tex]\[
y = 1
\][/tex]
2. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = \frac{1}{4}(0) + 2
\][/tex]
[tex]\[
y = 0 + 2
\][/tex]
[tex]\[
y = 2
\][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[
y = \frac{1}{4}(4) + 2
\][/tex]
[tex]\[
y = 1 + 2
\][/tex]
[tex]\[
y = 3
\][/tex]
Now we can fill in the table with the calculated values:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-4 & 1.0 \\
\hline
0 & 2.0 \\
\hline
4 & 3.0 \\
\hline
\end{tabular}
\][/tex]
