The best line of fit y = 9.37x + 5 represents the tolls you pay after driving a specific number of miles. What prediction can be made

Question

You spend )42 to drive 100 miles
If you drove 10 miles you would pay $42
You can spend less than $30 to go 75 miles
You can drive 50 miles and spend less than $20

Answer 1

To analyze the predictions based on the line of fit \( y = 9.37x + 5 \), where \( y \) represents the tolls paid and \( x \) represents the number of miles driven, we can evaluate each statement one by one.

1. You spend $42 to drive 100 miles:

   • Substitute \( x = 100 \) into the equation: \[ y = 9.37(100) + 5 = 937 + 5 = 942 \] So for 100 miles, you would pay $942, not $42. This statement is false.

2. If you drove 10 miles you would pay $42:

   • Substitute \( x = 10 \) into the equation: \[ y = 9.37(10) + 5 = 93.7 + 5 = 98.7 \] So for 10 miles, you would pay approximately $98.70, not $42. This statement is false.

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

   • Substitute \( x = 75 \) into the equation: \[ y = 9.37(75) + 5 = 703.25 + 5 = 708.25 \] So for 75 miles, you would pay approximately $708.25, which is much more than $30. This statement is false.

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

   • Substitute \( x = 50 \) into the equation: \[ y = 9.37(50) + 5 = 468.5 + 5 = 473.5 \] So for 50 miles, you would pay approximately $473.50, which is significantly more than $20. This statement is false.

Based on our calculations, all four statements provided about tolls based on the line of fit are false.

Answer 2

Sorry the equation is y = 0.37x + 5

Answer 3

No problem! Let's consider the corrected equation \( y = 0.37x + 5 \). We'll evaluate the claims based on this new equation.

1. You spend $42 to drive 100 miles:

   • Substitute \( x = 100 \): \[ y = 0.37(100) + 5 = 37 + 5 = 42 \]
   • The result is $42. This statement is true.

2. If you drove 10 miles you would pay $42:

   • Substitute \( x = 10 \): \[ y = 0.37(10) + 5 = 3.7 + 5 = 8.7 \]
   • The result is approximately $8.70, not $42. This statement is false.

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

   • Substitute \( x = 75 \): \[ y = 0.37(75) + 5 = 27.75 + 5 = 32.75 \]
   • The result is approximately $32.75, which is not less than $30. This statement is false.

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

   • Substitute \( x = 50 \): \[ y = 0.37(50) + 5 = 18.5 + 5 = 23.5 \]
   • The result is approximately $23.50, which is not less than $20. This statement is false.

Summary:

• True: You spend $42 to drive 100 miles.
• False: If you drove 10 miles you would pay $42.
• False: You can spend less than $30 to go 75 miles.
• False: You can drive 50 miles and spend less than $20.