To solve this problem, we need to find the line of best fit from the scatter plot and use it to predict how many hot cocoas Josue would sell if the temperature were 54°F.

Step-by-Step Solution

1. Determine the Equation of the Line of Best Fit: From the graph, the line of best fit appears to have a negative slope, suggesting that as temperature increases, the number of hot cocoas sold decreases. Let’s approximate the slope and y-intercept based on the points labeled on the line.

   By observing points on the line:

   • At $(0, 104)$, the number of hot cocoas sold is 104 when the temperature is 0°F.
   • At $(36, 62)$, the number of hot cocoas sold is 62 when the temperature is 36°F.

2. Calculate the Slope (m): The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting values from points $(0, 104)$ and $(36, 62)$: $m = \frac{62 - 104}{36 - 0} = \frac{-42}{36} = -1.17$

3. Determine the Y-Intercept (b): Since the line passes through $(0, 104)$, we can use this point as the y-intercept, so $b = 104$.

4. Formulate the Equation: The equation of the line is: $y = -1.17x + 104$

5. Predict the Number of Hot Cocoas Sold at 54°F: Substitute $x = 54$ into the equation: $y = -1.17(54) + 104$ $y = -63.18 + 104$ $y \approx 40.82$

   Rounding to the nearest whole number, Josue would sell approximately 41 hot cocoas at 54°F.

Would you like more details on this solution or have any questions?

Related Questions

1. How would the line of best fit change if more data points were added at higher temperatures?
2. Can we interpret the slope to understand how temperature affects hot cocoa sales?
3. What would be the predicted number of hot cocoas sold at a temperature of 10°F?
4. How does interpolation differ from extrapolation in the context of this problem?
5. What statistical methods could we use to verify the accuracy of our line of best fit?

Tip

When predicting values from a line of best fit, remember that the line is an approximation. Extreme values or outliers might make predictions less accurate.