To analyze the line of best fit, which is given by the equation \(y = 50x + 75\), where \(y\) represents the price of the trip, and \(x\) represents the number of hours of the trip, we can find the price of the trip for different lengths.
Let's evaluate each statement:
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Charles pays $300 for a 3-hour trip.
To find the price for a 3-hour trip: \[ y = 50(3) + 75 = 150 + 75 = 225 \] So, this statement is false because he would pay $225, not $300. -
Charles can go on a 1-hour fishing trip for less than $100.
To find the price for a 1-hour trip: \[ y = 50(1) + 75 = 50 + 75 = 125 \] This statement is false because he would pay $125, which is not less than $100. -
For $200, Charles can travel for 2 hours.
To find the price for a 2-hour trip: \[ y = 50(2) + 75 = 100 + 75 = 175 \] This statement is true because $200 is greater than $175, meaning he can afford a 2-hour trip. -
Charles can take a 6-hour trip for less than $400.
To find the price for a 6-hour trip: \[ y = 50(6) + 75 = 300 + 75 = 375 \] This statement is true because $375 is indeed less than $400.
Based on this analysis, both the third and fourth statements are valid, but since the question asks for a single prediction, the strongest prediction based on the line of best fit is that Charles can take a 6-hour trip for less than $400.