To analyze the line of best fit given by the equation \( y = 50x + 75 \), we can substitute specific values of \( x \) (the number of hours of the trip) to find the corresponding price \( y \).
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For a 6-hour trip (\( x = 6 \)): \[ y = 50(6) + 75 = 300 + 75 = 375 \] This prediction means that Charles can take a 6-hour trip for $375.
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For a 2-hour trip (\( x = 2 \)): \[ y = 50(2) + 75 = 100 + 75 = 175 \] This prediction means that for $200, Charles can actually only travel for 2 hours at a price of $175.
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For a 1-hour trip (\( x = 1 \)): \[ y = 50(1) + 75 = 50 + 75 = 125 \] This prediction means that Charles can go on a 1-hour trip for $125 which is not less than $100.
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For a 3-hour trip (\( x = 3 \)): \[ y = 50(3) + 75 = 150 + 75 = 225 \] This prediction means that Charles pays $225 for a 3-hour trip, not $300.
Now let's analyze each response:
- Charles can take a 6-hour trip for less than $400. (True: $375 is less than $400)
- For $200, Charles can travel for 2 hours. (False: It’s actually $175 for 2 hours)
- Charles can go on a 1-hour trip for less than $100. (False: It’s actually $125 for 1 hour)
- Charles pays $300 for a 3-hour trip. (False: He actually pays $225)
Thus, the correct statement based on the line of best fit is:
Charles can take a 6-hour trip for less than $400.
1 answer