Questions: Amount of money spent on entertainment (in dollars) Use the equation of the line of best fit, y=1.82 x+11.36, to answer the questions below. Give exact answers, not rounded approximations. (a) For an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment? (b) What is the predicted amount of money spent on entertainment for a student who doesn't work any hours? (c) What is the predicted amount of money spent on entertainment for a student who works 8 hours?

Amount of money spent on entertainment (in dollars) Use the equation of the line of best fit, y=1.82 x+11.36, to answer the questions below. Give exact answers, not rounded approximations. (a) For an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment? (b) What is the predicted amount of money spent on entertainment for a student who doesn't work any hours? (c) What is the predicted amount of money spent on entertainment for a student who works 8 hours?
Transcript text: Amount of money spent on entertainment (in dollars) Use the equation of the line of best fit, $y=1.82 x+11.36$, to answer the questions below. Give exact answers, not rounded approximations. \begin{tabular}{|l|l|} \hline \begin{tabular}{l} (a) For an increase of one hour in time worked, what is the \\ predicted increase in the amount of money spent on \\ entertainment? \end{tabular} & $\$ \square$ \\ \hline \begin{tabular}{l} (b) What is the predicted amount of money spent on \\ entertainment for a student who doesn't work any hours? \end{tabular} & $\$ \square$ \\ \hline \begin{tabular}{l} (c) What is the predicted amount of money spent on \\ entertainment for a student who works 8 hours? \end{tabular} & $\$ \square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Find the predicted increase in the amount of money spent on entertainment for an increase of one hour in time worked.

The equation of the line of best fit is given as \(y = 1.82x + 11.36\), where \(y\) represents the amount of money spent on entertainment and \(x\) represents the number of hours worked. The slope of the line is 1.82, which represents the change in \(y\) for every unit change in \(x\). In this context, the slope represents the predicted increase in the amount of money spent on entertainment for every one hour increase in time worked. Therefore, for an increase of one hour in time worked, the predicted increase in the amount of money spent on entertainment is $1.82.

Step 2: Find the predicted amount of money spent on entertainment for a student who doesn't work any hours.

If a student doesn't work any hours, then \(x = 0\). Substituting \(x = 0\) into the equation \(y = 1.82x + 11.36\), we get:

\(y = 1.82(0) + 11.36 = 11.36\).

So, the predicted amount of money spent on entertainment for a student who doesn't work any hours is $11.36.

Step 3: Find the predicted amount of money spent on entertainment for a student who works 8 hours.

If a student works 8 hours, then \(x = 8\). Substituting \(x = 8\) into the equation \(y = 1.82x + 11.36\), we get:

\(y = 1.82(8) + 11.36 = 14.56 + 11.36 = 25.92\).

So, the predicted amount of money spent on entertainment for a student who works 8 hours is $25.92.

Final Answer

(a) \(\boxed{\$1.82}\) (b) \(\boxed{\$11.36}\) (c) \(\boxed{\$25.92}\)

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