Question

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

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

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

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

You can spend $42 to drive 100 miles.

Answer 1

To make predictions based on the line of best fit equation \( y = 0.37z + 5 \), where \( y \) represents the tolls paid and \( z \) is the number of miles driven, we can substitute different values of \( z \) to find the corresponding tolls \( y \).

1. **For 50 miles**:
\[
y = 0.37(50) + 5 = 18.5 + 5 = 23.5
\]
So, you would pay $23.50 for driving 50 miles, which means you cannot spend less than $20.

2. **For 75 miles**:
\[
y = 0.37(75) + 5 = 27.75 + 5 = 32.75
\]
So, you would spend $32.75 to drive 75 miles, which means you cannot spend less than $30.

3. **For 10 miles**:
\[
y = 0.37(10) + 5 = 3.7 + 5 = 8.7
\]
So, if you drove 10 miles, you would pay $8.70, much less than $42.

4. **For 100 miles**:
\[
y = 0.37(100) + 5 = 37 + 5 = 42
\]
So, you can spend $42 to drive 100 miles.

Given these calculations, the correct prediction from the provided options is:

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