To use the line of best fit, given by the equation \( y = 0.37x + 5 \), we need to identify what \( x \) and \( y \) represent. Here, \( x \) is the number of miles driven, and \( y \) represents the toll paid.
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For the statement, "If you drive 10 miles, you would pay $42": Plugging in \( x = 10 \) into the equation: \[ y = 0.37(10) + 5 = 3.7 + 5 = 8.7 \] This means if you drive 10 miles, you would pay $8.70, not $42. Therefore, the statement is incorrect according to the model.
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For the statement, "You can spend less than $30 to go 75 miles": Plugging in \( x = 75 \) into the equation: \[ y = 0.37(75) + 5 = 27.75 + 5 = 32.75 \] This means to drive 75 miles, you would pay approximately $32.75, which is more than $30. Hence, this statement is also incorrect according to the model.
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For the statement, "You can spend $42 to drive 100 miles": Plugging in \( x = 100 \) into the equation: \[ y = 0.37(100) + 5 = 37 + 5 = 42 \] This statement is correct, according to the model.
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For the statement, "You can drive 50 miles and spend less than $20": Plugging in \( x = 50 \) into the equation: \[ y = 0.37(50) + 5 = 18.5 + 5 = 23.5 \] This means to drive 50 miles, you would pay approximately $23.50, which is greater than $20. Hence, this statement is also incorrect according to the model.
Summary of Findings:
- The only prediction that aligns with the line of best fit is that you can spend $42 to drive 100 miles.
- The other statements regarding 10 miles, 75 miles, and 50 miles do not hold true according to the linear model provided.