To make predictions based on the line of best fit given by the equation \(y = 34x + 2\), where \(y\) represents the number of miles and \(x\) represents the number of gallons of gas, we can substitute the values of \(x\) into the equation.
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For 12 gallons: \[ y = 34(12) + 2 = 408 + 2 = 410 \text{ miles} \] So, a car can go 410 miles on 12 gallons of gas.
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For 15 gallons: \[ y = 34(15) + 2 = 510 + 2 = 512 \text{ miles} \] So, a car can go 512 miles on 15 gallons of gas.
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For 20 gallons: \[ y = 34(20) + 2 = 680 + 2 = 682 \text{ miles} \] So, a car can go 682 miles on 20 gallons of gas.
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For 3 gallons: \[ y = 34(3) + 2 = 102 + 2 = 104 \text{ miles} \] So, a car can go 104 miles on 3 gallons of gas.
Now we can evaluate the predictions given in the options:
- A car can go 400 miles on 12 gallons of gas. (False, it's 410 miles)
- A car can go over 500 miles on 15 gallons of gas. (True, it's 512 miles)
- With 20 gallons of gas, a car can travel over 700 miles. (False, it's 682 miles)
- A car can go less than 100 miles on 3 gallons of gas. (False, it's 104 miles)
The correct prediction based on the data is: A car can go over 500 miles on 15 gallons of gas.