Question

A) A car can go a certain number of miles per gallon of gas. The line of best fit that represents
these data is y = 34x + 2, where the number of miles is based on the number of gallons of gas.
Using this linear model, what prediction can be drawn? (1 point)
A car can go 400 miles on 12 gallons of gas.
With 20 gallons of gas, a car can travel over 700 miles.
A car can go less than 100 miles on 3 gallons of gas.
A car can go over 500 miles on 15 gallons of gas.

Answer 1

To determine the predictions based on the linear model \( y = 34x + 2 \), where \( y \) represents the miles traveled and \( x \) represents the number of gallons of gas, we can evaluate each option:

1. **A car can go 400 miles on 12 gallons of gas.**
\[
y = 34(12) + 2 = 408 + 2 = 410 \text{ miles}
\]
This statement is **not true** since 410 miles is greater than 400 miles.

2. **With 20 gallons of gas, a car can travel over 700 miles.**
\[
y = 34(20) + 2 = 680 + 2 = 682 \text{ miles}
\]
This statement is **not true** since 682 miles is less than 700 miles.

3. **A car can go less than 100 miles on 3 gallons of gas.**
\[
y = 34(3) + 2 = 102 + 2 = 104 \text{ miles}
\]
This statement is **not true** since 104 miles is greater than 100 miles.

4. **A car can go over 500 miles on 15 gallons of gas.**
\[
y = 34(15) + 2 = 510 + 2 = 512 \text{ miles}
\]
This statement is **true** since 512 miles is greater than 500 miles.

Based on this analysis, the correct prediction is:
**A car can go over 500 miles on 15 gallons of gas.**