To determine the equation of the line of best fit for the ice cream sales data and draw a conclusion from it, let’s analyze the options provided.
- Line Equations:
- \( y = 10x \)
- \( y = 30x - 150 \)
- \( y = -100x + 30 \)
In the context of ice cream sales, \( y \) generally represents the amount of ice cream sold, while \( x \) represents temperature.
- Assessing Each Equation:
- \( y = 10x \): This indicates a positive relationship. As temperature increases, ice cream sales increase proportionally.
- \( y = 30x - 150 \): This also suggests a positive relationship, but with an intercept that might imply sales start at a negative value when the temperature is very low, which doesn’t make practical sense.
- \( y = -100x + 30 \): This indicates a negative relationship, meaning as temperature increases, ice cream sales decrease, which is contrary to what we expect.
Given that ice cream sales are typically expected to rise as temperatures rise (especially on warm days), the most appropriate equation that supports this relationship is likely \( y = 10x \) or \( y = 30x - 150 \), with the former being the most straightforward interpretation of a direct proportionality.
- Conclusion:
- As the temperature goes up, ice cream sales go up is a valid conclusion.
- The statement "The temperature rising causes ice cream sales to go up" indicates a causal relationship which suggests that rising temperature leads directly to increased sales, which could be seen as oversimplified.
In conclusion, based on the analysis of the equations, it seems that the best fit is likely \( y = 10x \), indicating that as temperature rises, ice cream sales increase. The more cautious and generally accepted conclusion is that as the temperature goes up, ice cream sales go up.