Charles wants to go on a fishing trip. The price of the excursion varies based on the length of the trip. The line of best fit for these data is y=50x+75

𝑦
=
50
𝑥
+
75
, where the price of the trip is based on the number of hours of the trip. What prediction can be made about the length of his trip based on the line of best fit?(1 point)
Responses

Charles can take a 6-hour trip for less than $400.
Charles can take a 6-hour trip for less than $400.

For $200, Charles can travel for 2 hours.
For $200, Charles can travel for 2 hours.

Charles pays $300 for a 3-hour trip.
Charles pays $300 for a 3-hour trip.

Charles can go on a 1-hour fishing trip for less than $100.

1 answer

To analyze the predictions based on the line of best fit equation \( y = 50x + 75 \), we need to compute the price for different lengths of trips (where \( x \) represents the number of hours).

  1. For a 6-hour trip: \[ y = 50(6) + 75 = 300 + 75 = 375 \] So, the price for a 6-hour trip is $375, which is less than $400. (This statement is true)

  2. For a $200 price point (we need to solve \( y = 200 \)): \[ 200 = 50x + 75 \] \[ 125 = 50x \quad \Rightarrow \quad x = \frac{125}{50} = 2.5 \] So, for $200, Charles can travel for 2.5 hours, not 2 hours. (This statement is false)

  3. For a 3-hour trip: \[ y = 50(3) + 75 = 150 + 75 = 225 \] So, the price for a 3-hour trip is $225, not $300. (This statement is false)

  4. For a 1-hour trip: \[ y = 50(1) + 75 = 50 + 75 = 125 \] So, the price for a 1-hour trip is $125, not less than $100. (This statement is false)

In conclusion, the true statement from the provided predictions is: Charles can take a 6-hour trip for less than $400.