Use the linear model to make a prediction. The line of best fit y=0.37x+5

Question

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

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

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

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

Answer 1

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

Let's evaluate the options provided:

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

   • Calculate \( y \) when \( x = 100 \): \[ y = 0.37(100) + 5 = 37 + 5 = 42 \]
   • This statement is true.

2. 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 statement is false because $32.75 is not less than $30.

3. 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 statement is false because $8.7 is not $42.

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

   • Calculate \( y \) when \( x = 50 \): \[ y = 0.37(50) + 5 = 18.5 + 5 = 23.5 \]
   • This statement is false because $23.5 is not less than $20.

The only true prediction based on the linear model is the first option: You can spend $42 to drive 100 miles.