To analyze the equation \( y = 2.5x + 5 \):
- y is the total time in minutes from when an order is placed until it is delivered.
- x is the number of miles between the shop and the delivery location.
From this equation, we can deduce the following:
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The term \( 2.5x \) represents the time taken for travel. Since the coefficient of \( x \) is \( 2.5 \), this means that for each mile traveled, it takes an additional 2.5 minutes of delivery time.
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The constant term \( 5 \) represents the preparation time, which is the time taken by the shop to prepare the food for delivery.
With this understanding, we can evaluate the statements:
A. On average, it takes the delivery person 2.5 minutes to travel 1 mile.
- This statement is correct because based on \( 2.5x \), it takes 2.5 minutes to travel 1 mile.
B. The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.
- This statement is incorrect because the preparation time is represented by the constant \( 5 \), not \( 2.5 \).
C. On average, it takes the delivery person 5 minutes to travel 1 mile.
- This statement is incorrect because it takes 2.5 minutes to travel 1 mile, not 5 minutes.
D. On average, the delivery person travels 2.5 miles every 1 minute.
- This statement is incorrect because if it takes 2.5 minutes to travel 1 mile, it cannot be true that 2.5 miles are covered in 1 minute.
E. The average amount of time the shop needs to prepare the food for delivery is 5 minutes.
- This statement is correct because the constant term in the equation, 5, represents the preparation time.
F. On average, the delivery person travels 5 miles every 1 minute.
- This statement is incorrect because it takes 2.5 minutes to travel 1 mile, meaning the delivery person travels 0.4 miles in 1 minute.
Thus, the two correct statements according to the model are:
A. On average, it takes the delivery person 2.5 minutes to travel 1 mile.
E. The average amount of time the shop needs to prepare the food for delivery is 5 minutes.