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To solve this problem, we need to interpret the line of best fit on the scatter plot. The question asks for a prediction of the number of hot cocoas Kennedy would sell if the day’s high temperature were 40°F.

### Step 1: Understand the Line of Best Fit
The line of best fit is drawn through three points given on the plot:
1. \((0, 84)\)
2. \((8, 77)\)
3. \((16, 70)\)
4. \((24, 63)\)

This line shows a linear relationship between temperature and the number of cocoas sold, suggesting that as temperature increases, the number of cocoas sold decreases.

### Step 2: Calculate the Equation of the Line
We can use two points to determine the slope (\(m\)) of the line:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using points \((0, 84)\) and \((24, 63)\):
\[
m = \frac{63 - 84}{24 - 0} = \frac{-21}{24} = -0.875
\]

Now we can use the slope-intercept form of a line, \(y = mx + b\), where \(b\) is the y-intercept. Since the line passes through \((0, 84)\), the y-intercept \(b\) is 84. So, the equation of the line of best fit is:
\[
y = -0.875x + 84
\]

### Step 3: Substitute 40°F into the Equation
Now, substitute \(x = 40\) (temperature in °F) to find the predicted number of cocoas:
\[
y = -0.875(40) + 84
\]
\[
y = -35 + 84
\]
\[
y = 49
\]

### Answer
Based on the line of best fit, Kennedy would be predicted to sell **49 hot cocoas** if the day’s high temperature were 40°F.

Would you like further details on any of these steps?

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### Related Questions
1. What would be the predicted number of cocoas sold if the temperature was 50°F?
2. How would the equation change if one of the data points was altered?
3. Can we use a quadratic model instead, and would it fit the data better?
4. What does the slope of \(-0.875\) represent in this context?
5. How does the y-intercept of 84 relate to the context of this problem?

#### Tip
In linear models, interpreting the slope and intercept helps to understand the practical meaning of changes in variables in real-world scenarios.

Based on the line of best fit, how many hot cocoas would you predict Kennedy to sell if the day’s high temperature were 40°F?

Learn how to predict hot cocoa sales based on temperature using the line of best fit. This problem involves analyzing a scatter plot and calculating the slope-intercept form to estimate cocoa sales at different temperatures, suitable for Grades 8-10.

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