To analyze the line of best fit, which is given by the equation \( y = 50x + 75 \), where \( y \) is the price of the trip and \( x \) is the length of the trip in hours, we can substitute values for \( y \) to predict the values of \( x \).
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To find the length of the trip for a price of $200: \[ 200 = 50x + 75 \] \[ 200 - 75 = 50x \] \[ 125 = 50x \] \[ x = \frac{125}{50} = 2.5 \] So, for $200, Charles can travel for 2.5 hours.
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To find the cost for a 6-hour trip: \[ y = 50(6) + 75 = 300 + 75 = 375 \] This means that for a 6-hour trip, the cost is $375, which is less than $400.
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To check the cost for a 3-hour trip: \[ y = 50(3) + 75 = 150 + 75 = 225 \] Therefore, Charles pays $225 for a 3-hour trip.
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To find the cost for a 1-hour trip: \[ y = 50(1) + 75 = 50 + 75 = 125 \] Thus, for a 1-hour trip, the cost is $125, which is indeed more than $100.
Based on the calculations above, we can determine that the prediction about the length of Charles' trip would be correct for the options provided:
- "For $200, Charles can travel for 2 hours." (This is incorrect because he can travel for 2.5 hours.)
- "Charles can take a 6-hour trip for less than $400." (This is correct as it costs $375.)
- "Charles pays $300 for a 3-hour trip." (This is incorrect; he pays $225.)
- "Charles can go on a 1-hour fishing trip for less than $100." (This is incorrect; he pays $125.)
Based on this analysis, the correct prediction is: Charles can take a 6-hour trip for less than $400.
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