Question

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

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

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.

Answer 1

To make predictions using the line of best fit \( y = 0.37x + 5 \), we can plug in the values of \( x \) (the number of miles driven) to find the corresponding toll ( \( y \) ).

1. **For 50 miles:**
\( y = 0.37(50) + 5 \)
\( y = 18.5 + 5 \)
\( y = 23.5 \)
Therefore, you would pay $23.50 for 50 miles.

2. **For 10 miles:**
\( y = 0.37(10) + 5 \)
\( y = 3.7 + 5 \)
\( y = 8.7 \)
Therefore, you would pay $8.70 for 10 miles.

3. **For 100 miles:**
\( y = 0.37(100) + 5 \)
\( y = 37 + 5 \)
\( y = 42 \)
Therefore, you would pay $42 for 100 miles.

4. **For 75 miles:**
\( y = 0.37(75) + 5 \)
\( y = 27.75 + 5 \)
\( y = 32.75 \)
Therefore, you would pay $32.75 for 75 miles.

Now evaluating the given responses:

1. **You can drive for 50 miles and spend less than $20.**
(False, you would pay $23.50)

2. **If you drove 10 miles, you would pay $42.**
(False, you would pay $8.70)

3. **You can spend $42 to drive 100 miles.**
(True, you would pay exactly $42)

4. **You can spend less than $30 to go 75 miles.**
(False, you would pay $32.75)

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