Question

Suppose you start with a full tank of gas (14 gallons) in your truck. After driving 4 hours, you now have 2

gallons left.
If x is the number of hours you have been driving, then y is the number of gallons left in the tank.
At what rate is the gas left in the tank changing? State your answer as a reduced fraction.
gallons per hour
Find an equation of a line in the form y = mx + b that describes the amount of gas in your tank.
Y =

Answer 1

a) -3 gallons per hour

b) y = -3x +14

Explanation:

Rate of change is computed by dividing the amount of change by the interval over which it occurred.

a)

Here the amount of gas decreased from 14 to 2 gallons, so a decrease of 14-2 = 12 gallons. That occurred over a 4-hour period, so the rate of change is (-12 gallons)/(4 hours) = -3 gallons/hour.

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b)

The initial amount was 14 gallons, so the equation for the line describing remaining gas will be ...

y = -3x +14 . . . . gas in the tank after x hours