Given the equation of the line of best fit: [tex]\( y = 0.4 x + 23.35 \)[/tex], we will use it to determine the predicted amount of money spent on entertainment for each number of hours worked listed.
### Step-by-Step Calculation:
1. For [tex]\( x = 4.1 \)[/tex]:
[tex]\[
y = 0.4 \cdot 4.1 + 23.35 = 1.64 + 23.35 = 24.99
\][/tex]
2. For [tex]\( x = 4.4 \)[/tex]:
[tex]\[
y = 0.4 \cdot 4.4 + 23.35 = 1.76 + 23.35 = 25.11
\][/tex]
3. For [tex]\( x = 5.6 \)[/tex]:
[tex]\[
y = 0.4 \cdot 5.6 + 23.35 = 2.24 + 23.35 = 25.59
\][/tex]
4. For [tex]\( x = 6.9 \)[/tex]:
[tex]\[
y = 0.4 \cdot 6.9 + 23.35 = 2.76 + 23.35 = 26.11
\][/tex]
5. For [tex]\( x = 7.0 \)[/tex]:
[tex]\[
y = 0.4 \cdot 7.0 + 23.35 = 2.8 + 23.35 = 26.15
\][/tex]
6. For [tex]\( x = 8.1 \)[/tex]:
[tex]\[
y = 0.4 \cdot 8.1 + 23.35 = 3.24 + 23.35 = 26.59
\][/tex]
7. For [tex]\( x = 9.1 \)[/tex]:
[tex]\[
y = 0.4 \cdot 9.1 + 23.35 = 3.64 + 23.35 = 26.99
\][/tex]
8. For [tex]\( x = 11.1 \)[/tex]:
[tex]\[
y = 0.4 \cdot 11.1 + 23.35 = 4.44 + 23.35 = 27.79
\][/tex]
9. For [tex]\( x = 11.9 \)[/tex]:
[tex]\[
y = 0.4 \cdot 11.9 + 23.35 = 4.76 + 23.35 = 28.11
\][/tex]
### Final Table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of hours worked, } x & \text{Amount spent on entertainment, } y \text{ (in dollars)} \\
\hline
4.1 & 24.99 \\
4.4 & 25.11 \\
5.6 & 25.59 \\
6.9 & 26.11 \\
7.0 & 26.15 \\
8.1 & 26.59 \\
9.1 & 26.99 \\
11.1 & 27.79 \\
11.9 & 28.11 \\
\hline
\end{array}
\][/tex]
These values are the exact amounts of money spent on entertainment according to the line of best fit.
