Use the linear model to make a prediction. The line of the best fit y=).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?

Question

D: You can spend less than $30 to go 75 miles
A:If you drove 10 miles, you would pay $42.
C:You can spend $42 to drive 100 miles.

Answer 1

To make a prediction using the line of best fit given by the equation \( y = 0.37x + 5 \), we need to understand how the equation works:

• \( y \) represents the total toll cost.
• \( x \) represents the number of miles driven.
• The slope (0.37) indicates the cost per mile, and the intercept (5) represents a base fee.

Let's evaluate the predictions based on the given equation.

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

   • Calculate \( y \) when \( x = 75 \): \[ y = 0.37(75) + 5 = 27.75 + 5 = 32.75 \] This prediction is incorrect since $32.75 is greater than $30.

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

   • Calculate \( y \) when \( x = 10 \): \[ y = 0.37(10) + 5 = 3.7 + 5 = 8.7 \] This prediction is incorrect since $8.70 is much less than $42.

3. C: You can spend $42 to drive 100 miles.

   • Calculate \( y \) when \( x = 100 \): \[ y = 0.37(100) + 5 = 37 + 5 = 42 \] This prediction is correct since driving 100 miles will cost exactly $42.

Therefore, the correct prediction based on the line of best fit is C: You can spend $42 to drive 100 miles.