Subjects algebra

Temperature Prediction 4A8B39

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1. **State the problem:** We want to predict the day's high temperature $x$ when Malika sold 57 hot cocoas, based on the line of best fit from the scatter plot. 2. **Understand the variables:** The x-axis represents the high temperature in degrees Fahrenheit, and the y-axis represents the number of hot cocoas sold. 3. **Identify the line of best fit:** The line trends downward, indicating a negative slope. We can estimate two points on the line to find its equation. 4. **Estimate two points on the line:** From the graph, approximate points are $(6, 96)$ and $(33, 69)$. 5. **Calculate the slope $m$ of the line:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{69 - 96}{33 - 6} = \frac{-27}{27} = -1$$ 6. **Find the equation of the line:** Using point-slope form with point $(6, 96)$: $$y - 96 = -1(x - 6)$$ $$y - 96 = -x + 6$$ $$y = -x + 102$$ 7. **Predict the temperature for $y=57$ hot cocoas sold:** $$57 = -x + 102$$ $$x = 102 - 57$$ $$x = 45$$ 8. **Interpretation:** If Malika sold 57 hot cocoas, the predicted high temperature is $45$ degrees Fahrenheit.