To analyze the situation, we can use the equation of the line of best fit given as \( y = 50x + 75 \), where \( y \) represents the price of the fishing trip and \( x \) is the number of hours.
First, let's interpret the equation:
- The base cost of the trip starts at $75 (the constant term).
- For each hour of fishing (each unit increase in \( x \)), the cost increases by $50.
Now, let's evaluate each of the predictions you provided:
-
Charles pays $300 for a 3-hour trip: \[ y = 50(3) + 75 = 150 + 75 = 225 \] This result indicates that the cost for a 3-hour trip should be $225, not $300. Therefore, this prediction does not hold true.
-
Charles can take a 6-hour trip for less than $400: \[ y = 50(6) + 75 = 300 + 75 = 375 \] Since $375 is indeed less than $400, this prediction is true.
-
Charles can travel for 2 hours: \[ y = 50(2) + 75 = 100 + 75 = 175 \] This indicates that the price for a 2-hour trip is $175. Yes, Charles can travel for 2 hours but it will cost him $175.
-
Charles can go on a 1-hour fishing trip for less than $100: \[ y = 50(1) + 75 = 50 + 75 = 125 \] The cost for a 1-hour trip is $125, which is not less than $100. Thus, this prediction is false.
Summary of Predictions:
- Prediction 1: False ($225 instead of $300)
- Prediction 2: True ($375 is less than $400)
- Prediction 3: True (He can travel for 2 hours, but it costs $175)
- Prediction 4: False ($125 instead of less than $100)
So, the only correct prediction is that Charles can take a 6-hour trip for less than $400.