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

Question

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

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

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

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

Answer 1

To make predictions based on the line of best fit \(y = 50x + 75\), we can analyze the options given:

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

   • Plugging \(x = 2\) into the equation: \[ y = 50(2) + 75 = 100 + 75 = 175 \] This means that for 2 hours, the cost is $175, which is less than $200, so this option could be true.

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

   • Plugging \(x = 6\) into the equation: \[ y = 50(6) + 75 = 300 + 75 = 375 \] So for a 6-hour trip, the cost is $375, which is less than $400. This option is also true.

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

   • Plugging \(x = 3\) into the equation: \[ y = 50(3) + 75 = 150 + 75 = 225 \] This means he actually pays $225 for a 3-hour trip, so this statement is false.

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

   • Plugging \(x = 1\) into the equation: \[ y = 50(1) + 75 = 50 + 75 = 125 \] This means he would pay $125 for a 1-hour trip, so this statement is false.

Based on the analysis, the true predictions are:

• For $200, Charles can travel for 2 hours.
• Charles can take a 6-hour trip for less than $400.

Both the first and second options could be considered correct predictions based on the data provided.