A driver starts a trip with 30 gallons of gasoline in the tank of his car. The car burns 4 gallons for every 80 miles.

Question

Assuming that the amount of gasoline in the tank decreases linearly, write a linear function that relates the number of gallons G left in the tank after a journey of “d” miles. The choices are

A. G = 30 – (4/80) * d
B. G = 25 – (5/100) * d
C. G = 4 – (30/80) * d
D. G = 80 – (4/30) * d

Answer 1

Let's start by reviewing the slope-intercept formula:

y = mx + b

At the start of the journey, we have a full tank at 30 gallons and have yet to go anywhere. That means that our b is 30:

y = mx + 30

 

Now to focus on the slope. Every time the driver loses 4 gallons, 80 miles have passed. Written as rise/run, that means our slope looks like:

^-4/₈₀

So the equation looks like:

y = ^-4/₈₀ x + 30

 

Whichever choice matches up with the same equation is your answer.

Answer 2

The answer is A because you are decreasing your initial volume (30 gal) of gas with every mile driven at a rate of 4 gallons/80 miles.