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Question

Use the linear model to make a prediction. The line of best fit y=0.37x+5
represents the tolls you pay after driving a specific number of miles. What prediction can be made based on this line of best fit?(1 point)
Responses

You can drive for 50 miles and spend less than $20.
You can drive for 50 miles and spend less than $20.

You can spend $42 to drive 100 miles.
You can spend $42 to drive 100 miles.

If you drove 10 miles, you would pay $42.
If you drove 10 miles, you would pay $42.

You can spend less than $30 to go 75 miles.

1 answer

To make predictions using the linear model \( y = 0.37x + 5 \), where \( y \) is the toll and \( x \) is the number of miles driven, we can substitute different values of \( x \) to find the corresponding toll \( y \).

  1. For 50 miles (x = 50): \[ y = 0.37(50) + 5 = 18.5 + 5 = 23.5 \] The toll for driving 50 miles would be $23.50, which is more than $20.

  2. For 100 miles (x = 100): \[ y = 0.37(100) + 5 = 37 + 5 = 42 \] The toll for driving 100 miles would be $42.

  3. For 10 miles (x = 10): \[ y = 0.37(10) + 5 = 3.7 + 5 = 8.7 \] The toll for driving 10 miles would be $8.70, which is not $42.

  4. For 75 miles (x = 75): \[ y = 0.37(75) + 5 = 27.75 + 5 = 32.75 \] The toll for driving 75 miles would be $32.75, which is more than $30.

Based on this analysis, the only correct prediction from the provided responses is:

You can spend $42 to drive 100 miles.