Question

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

Charles pays $300 for a 3-hour trip.

1 answer

To make predictions based on the given line of best fit, $ y = 50x + 75 $, where $ y $ is the price and $ x $ is the number of hours of the trip, we can substitute the values of $ x $ to determine the corresponding prices.

Let's analyze each of the options:

Charles can take a 6-hour trip for less than $400.
- For $ x = 6 $:
  $ y = 50(6) + 75 = 300 + 75 = 375 $.
  This statement is true; $375 is less than $400.
For $200, Charles can travel for 2 hours.
- For $ x = 2 $:
  $ y = 50(2) + 75 = 100 + 75 = 175 $.
  This means $200 is more than needed, but he can travel for 2 hours for $175. The statement implies he can travel for 2 hours for exactly $200, which is not true.
Charles can go on a 1-hour fishing trip for less than $100.
- For $ x = 1 $:
  $ y = 50(1) + 75 = 50 + 75 = 125 $.
  This statement is false; $125 is not less than $100.
Charles pays $300 for a 3-hour trip.
- For $ x = 3 $:
  $ y = 50(3) + 75 = 150 + 75 = 225 $.
  This statement is false; he pays $225 for 3 hours, not $300.

The only true statement based on the line of best fit is:

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