To determine the function rule for the given table, we need to analyze how the pay corresponds to the hours worked.
Let's summarize the given data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Hours Worked} & \text{Pay (\$)} \\
\hline
2 & 11.50 \\
\hline
4 & 23.00 \\
\hline
6 & 34.50 \\
\hline
8 & 46.00 \\
\hline
\end{array}
\][/tex]
We need to find a linear relationship of the form [tex]\( p = r \cdot h \)[/tex], where:
- [tex]\( p \)[/tex] is the pay.
- [tex]\( h \)[/tex] is the hours worked.
- [tex]\( r \)[/tex] is the pay rate per hour.
To find the pay rate ([tex]\( r \)[/tex]), we can use one of the data pairs. Let's use the first pair (2, 11.50):
[tex]\[ 11.50 = r \cdot 2 \][/tex]
Solving for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{11.50}{2} \][/tex]
[tex]\[ r = 5.75 \][/tex]
So, the pay rate is [tex]\( 5.75 \)[/tex] dollars per hour.
Now we can write the function rule that describes this relationship:
[tex]\[ p = 5.75h \][/tex]
Next, let's verify that this rule works with the other data pairs:
1. For [tex]\( h = 4 \)[/tex]:
[tex]\[ p = 5.75 \cdot 4 \][/tex]
[tex]\[ p = 23.00 \][/tex]
2. For [tex]\( h = 6 \)[/tex]:
[tex]\[ p = 5.75 \cdot 6 \][/tex]
[tex]\[ p = 34.50 \][/tex]
3. For [tex]\( h = 8 \)[/tex]:
[tex]\[ p = 5.75 \cdot 8 \][/tex]
[tex]\[ p = 46.00 \][/tex]
Since the function rule [tex]\( p = 5.75h \)[/tex] fits all the data points correctly, this confirms that the rule is accurate.
Therefore, the correct function rule for the table is:
[tex]\[ p = 5.75h \][/tex]
