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

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 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.

Answer 1

To determine which response can be made based on the line of best fit \( y = 50x + 75 \), where \( y \) is the price and \( x \) is the number of hours, we can analyze each statement:

1. **For $200, Charles can travel for 2 hours.**
\[
y = 50x + 75 \implies 200 = 50(2) + 75 \implies 200 = 100 + 75 \implies 200 \neq 175
\]
This statement is **false**.

2. **Charles can go on a 1-hour fishing trip for less than $100.**
\[
y = 50(1) + 75 = 50 + 75 = 125
\]
This statement is **false** because the cost is $125, not less than $100.

3. **Charles can take a 6-hour trip for less than $400.**
\[
y = 50(6) + 75 = 300 + 75 = 375
\]
This statement is **true** because the cost is $375, which is less than $400.

4. **Charles pays $300 for a 3-hour trip.**
\[
y = 50(3) + 75 = 150 + 75 = 225
\]
This statement is **false** because the cost is $225, not $300.

Based on this analysis, the only accurate prediction is:

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