The cost of a cab trip, y, is given by the table, where x is the number of miles traveled. Which THREE statements are correct?

Question

Responses
A The rate of change is $0.75.The rate of change is $0.75.
B A ten mile trip would cost $12.00.A ten mile trip would cost $12.00.
C The initial passenger fee is $2.00.The initial passenger fee is $2.00.
D A twenty mile trip would cost $17.00.A twenty mile trip would cost $17.00.
E The cost of a cab trip can be modeled by the function y = 1x + 2.The cost of a cab trip can be modeled by the function y = 1x + 2.

Answer 1

To determine which statements are correct based on the information provided, we need to analyze the cost of the cab trip in relation to the number of miles traveled, as indicated by the variables \( y \) (cost) and \( x \) (miles).

Assuming the cost structure follows a linear model of the form \( y = mx + b \), where \( m \) is the rate per mile and \( b \) is the initial fee (or base fare):

1. Statement A: The rate of change is $0.75.

   • This suggests a rate of $0.75 per mile. If we use $0.75 as the rate, we need to verify if it fits the other details provided.

2. Statement B: A ten mile trip would cost $12.00.

   • Using the presumed rate of $0.75 per mile with an initial fee of $2.00: \[ y = 0.75(10) + 2 = 7.5 + 2 = 9.50 \quad (\text{which is not } 12.00) \]

3. Statement C: The initial passenger fee is $2.00.

   • If we take the initial fee to be $2.00, this could potentially be correct, assuming the rate per mile is something else. We need to verify through other options.

4. Statement D: A twenty mile trip would cost $17.00.

   • Following the same calculation with $0.75: \[ y = 0.75(20) + 2 = 15.0 + 2 = 17.00 \quad (\text{which matches}) \]
   • However, if the base fee was not $2.00, then we still need to investigate.

5. Statement E: The cost of a cab trip can be modeled by the function y = 1x + 2.

   • Here, it appears that the cost per mile is $1.00 and an initial fee of $2.00. Checking this:
   • For a ten-mile trip: \[ y = 1(10) + 2 = 10 + 2 = 12 \]
   • For a twenty-mile trip: \[ y = 1(20) + 2 = 20 + 2 = 22 \]
   • The values do not adhere to the previously mentioned rates or results.

Assuming we can deduce the statements based on the information provided and sample calculations:

• Correct statements:
  • C: The initial passenger fee is $2.00. (Assuming a base fare)
  • D: A twenty-mile trip would cost $17.00 (if using a different rate).
  • B can be rejected because a ten-mile trip does not yield $12.00 using the rates mentioned.

Hence, only A, C, and D would be valid responses if rates were consistent.

Final correct statements are likely C, D, and potentially altering A to the correct $ per mile.