Here's the given rule: [tex]\( y = x + 3 \)[/tex].
We are provided with the rule and need to fill in the missing values in the table based on this rule.
### Step 1: Find [tex]\( y \)[/tex] when [tex]\( x = 4 \)[/tex]
Given [tex]\( x = 4 \)[/tex], we use the rule [tex]\( y = x + 3 \)[/tex]:
[tex]\[ y = 4 + 3 = 7 \][/tex]
So, when [tex]\( x = 4 \)[/tex], [tex]\( y = 7 \)[/tex].
### Step 2: Find [tex]\( x \)[/tex] when [tex]\( y = 8 \)[/tex]
Given [tex]\( y = 8 \)[/tex], we rearrange the rule [tex]\( y = x + 3 \)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ 8 = x + 3 \][/tex]
[tex]\[ x = 8 - 3 = 5 \][/tex]
So, when [tex]\( y = 8 \)[/tex], [tex]\( x = 5 \)[/tex].
### Step 3: Find [tex]\( y \)[/tex] when [tex]\( x = 5 \)[/tex]
Given [tex]\( x = 5 \)[/tex], we use the rule [tex]\( y = x + 3 \)[/tex]:
[tex]\[ y = 5 + 3 = 8 \][/tex]
So, when [tex]\( x = 5 \)[/tex], [tex]\( y = 8 \)[/tex].
### Tabulated Results
Now, we can complete the table and missing values:
[tex]\[
\begin{tabular}{cc}
$x$ & $y$ \\
\hline
4 & 7 \\
\square & 8 \\
5 & \square \\
\end{tabular}
\][/tex]
Inserting the calculated values:
[tex]\[
\begin{tabular}{cc}
$x$ & $y$ \\
\hline
4 & 7 \\
5 & 8 \\
5 & 8 \\
\end{tabular}
\][/tex]
Thus, the complete set of pairs is:
[tex]\[
(4, 7), (5, 8), (5, 8)
\][/tex]
