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The table and scatter plot show the number of hours worked, [tex]$x$[/tex], and the amount of money spent on entertainment, [tex]$y$[/tex], by each of 9 students.
The equation of the line of best fit is [tex]$y=0.4 x+23.35$[/tex].

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Number \\
of hours \\
worked, [tex]$x$[/tex]
\end{tabular} & \begin{tabular}{c}
Amount \\
spent on \\
entertainment, [tex]$y$[/tex] \\
(in dollars)
\end{tabular} \\
\hline 4.1 & 22.60 \\
\hline 4.4 & 27.61 \\
\hline 5.6 & 19.66 \\
\hline 6.9 & 29.18 \\
\hline 7.0 & 23.32 \\
\hline 8.1 & 33.50 \\
\hline 9.1 & 33.50 \\
\hline 11.1 & 24.93 \\
\hline 11.9 & 25.00 \\
\hline
\end{tabular}

Use the equation of the line of best fit to fill in the blanks below.
Give exact answers, not rounded approximations.
[tex]$\square$[/tex]



Answer :

GinnyAnswer
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.

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