Final answer:
The equation representing the remaining gallons of gas after traveling x miles is G = 12 - 0.08x, where G is the remaining gas and x is the distance traveled in miles.
Step-by-step explanation:
The question is asking for the equation that represents the remaining gallons of gas in Marcus's truck after traveling x miles. Let's look at the data provided: at 0 miles, Marcus starts with 12 gallons; after 1 mile, he has 11.92 gallons; after 2 miles, the remaining gas is 11.84 gallons; and after 3 miles, it is 11.76 gallons.
Since Marcus loses 0.08 gallons per mile (12 - 11.92 = 0.08), we can say that the consumption rate is 0.08 gallons/mile. The equation that represents the remaining gallons of gas 'G' after traveling 'x' miles can be formed by starting with the initial amount of gas and subtracting the amount used as he travels miles. Thus, the equation is:
G = 12 - 0.08x
Where G is the remaining gallons of gas and x is the number of miles traveled. This is a linear equation with a starting value (intercept) of 12 gallons and a slope of -0.08, indicating the rate at which the gas is being used per mile.