To understand what the slope means in the context of the cost function for the taxi ride, we need to analyze the function [tex]\( c(x) = 2x + 4.00 \)[/tex].
1. Identify the components of the function:
- [tex]\( c(x) \)[/tex]: This represents the total cost of the taxi ride.
- [tex]\( x \)[/tex]: This represents the number of minutes.
- [tex]\( 2x \)[/tex]: This term represents a cost that varies with the number of minutes [tex]\( x \)[/tex].
- [tex]\( 4.00 \)[/tex]: This is a constant term which represents a fixed base cost regardless of the duration of the ride.
2. Slope of the function:
The function [tex]\( c(x) = 2x + 4.00 \)[/tex] is in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- In this case, [tex]\( m = 2 \)[/tex].
3. Interpretation of the slope [tex]\( m = 2 \)[/tex]:
- The slope, [tex]\( m = 2 \)[/tex], indicates the rate at which the cost changes for each additional minute of the ride.
- Specifically, for each minute increase in the duration of the taxi ride, the cost increases by \[tex]$2.00.
4. Consider the given options:
- Option A: The rate of change of the cost of the taxi ride is \$[/tex]2.00 per minute.
- This option correctly describes the slope of the cost function.
- Option B: The taxi ride costs \[tex]$2.00 per trip.
- This option incorrectly describes the slope as a total cost per trip, which is not represented by the slope.
- Option C: The taxi ride costs a total of \$[/tex]4.00.
- This option only describes the y-intercept (initial base cost) of the function, not the slope.
- Option D: The rate of change of the cost of the taxi ride is \[tex]$4.00 per minute.
- This option incorrectly states the rate of change, which should be \$[/tex]2.00 per minute, not \[tex]$4.00.
5. Conclusion:
The correct interpretation of the slope in this context is that the rate of change of the cost of the taxi ride is \$[/tex]2.00 per minute.
Therefore, the correct answer is:
A. The rate of change of the cost of the taxi ride is \$2.00 per minute.
