Let's solve the questions using the given equation of the line of best fit: $y = -1.21x + 97.10$, where $x$ represents the average monthly temperature in °F and $y$ represents the monthly heating cost in dollars.

(a) Predicted heating cost for a month with an average temperature of $0^\circ \text{F}$:

Substitute $x = 0$ into the equation: $y = -1.21(0) + 97.10 = 97.10$ Answer: $97.10

(b) Predicted decrease in heating cost for an increase of one degree Fahrenheit:

The slope of the line ($-1.21$) represents the change in $y$ (heating cost) for a one-degree increase in $x$ (temperature). Thus: $\text{Decrease in cost} = 1.21 \, \text{dollars per degree}.$ Answer: $1.21

(c) Predicted heating cost for a month with an average temperature of $45^\circ \text{F}$:

Substitute $x = 45$ into the equation: $y = -1.21(45) + 97.10$ $y = -54.45 + 97.10 = 42.65$ Answer: $42.65

Would you like further clarification or additional breakdowns?

Here are 5 related questions to explore further:

1. How does the slope affect the trend in heating cost?
2. What would be the predicted cost for a temperature of $80^\circ \text{F}$?
3. How could this equation be used to determine at what temperature the heating cost reaches $0?
4. What is the importance of the $y$-intercept ($97.10$) in this context?
5. How does this linear model simplify the analysis of heating costs compared to other methods?

Tip: In any linear equation, the slope indicates the rate of change, while the intercept provides the starting value when the independent variable is zero!