To complete the table using the rule [tex]\( y = \frac{1}{4} x + 1 \)[/tex], we need to calculate the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex] value.
Step-by-step solution:
1. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = \frac{1}{4} \cdot 2 + 1
\][/tex]
[tex]\[
y = \frac{2}{4} + 1
\][/tex]
[tex]\[
y = 0.5 + 1
\][/tex]
[tex]\[
y = 1.5
\][/tex]
2. For [tex]\( x = 8 \)[/tex]:
[tex]\[
y = \frac{1}{4} \cdot 8 + 1
\][/tex]
[tex]\[
y = 2 + 1
\][/tex]
[tex]\[
y = 3
\][/tex]
3. For [tex]\( x = 12 \)[/tex]:
[tex]\[
y = \frac{1}{4} \cdot 12 + 1
\][/tex]
[tex]\[
y = 3 + 1
\][/tex]
[tex]\[
y = 4
\][/tex]
Thus, the completed table is as follows:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
2 & 1.5 \\
8 & 3.0 \\
12 & 4.0 \\
\end{array}
\][/tex]
This table shows the corresponding [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values based on the rule [tex]\( y = \frac{1}{4} x + 1 \)[/tex].
