To understand the meaning of the slope in this context, we should begin by recalling what a slope represents. The slope of a line measures the rate of change between the two variables being plotted; in this case, the "hours" and the "total number of cars washed."
Here are the steps to interpret the meaning of the slope:
1. Identify the Variables:
- The independent variable (x-axis) is the amount of time in hours.
- The dependent variable (y-axis) is the total number of cars washed.
2. Context of a Slope:
- The slope tells us how much the dependent variable (total number of cars washed) changes for each unit increase in the independent variable (hours).
3. Interpret the Given Slope:
- According to the problem, the slope of the line of best fit is 8.
- This means, on average, for every additional hour, the total number of cars washed increases by 8.
4. Analyze the Options:
- (A) The track team washed 8 cars in the first hour: This doesn't match the interpretation of a slope. It describes a specific number at a specific time, not a rate of change.
- (B) The track team washes about 8 cars each hour: This option aligns well with our understanding of the slope meaning that 8 cars are washed, on average, for each additional hour.
- (C) Each hour, the track team washes about 8 more cars than they did in the previous hour: This misinterprets the slope; the slope represents a consistent rate of change, not an increasing rate.
- (D) The track team washes cars for 8 hours: This doesn't relate to what a slope represents. It is about the duration, not the rate at which cars are washed.
5. Determine the Appropriate Answer:
- The slope of 8 means the rate at which the number of cars washed increases with time. Therefore, the best interpretation is that the track team washes about 8 cars for each hour.
The option that accurately reflects this interpretation is:
(B) The track team washes about 8 cars each hour.
