Suppose you start with a full tank of gas (20 gallons) in your truck.

Question

After driving 5 hours, you now have 9 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 your truck using gas? 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.     

Answer 1

Lets dissect this and make it a bit simpler.

Part 1:

#1- How much gas did you use in those 5hrs?

In 5 hrs you went from having 20 gallons to having 9 gallons. 20-9= 11 gallons used

#2- How many gallons did you use per hour?

11 gallons in 5 hours> 11 gallons/5 hours= 2.2 or 2 1/5 gallons per hour

Part 2:

Time to write the equation:

Find an equation of a line in the form y = mx + b

Lets simplify,

x= time and y= gallons left

At 0 time when the car hasn't moved. You still have 20 gallons so (0, 20) is one point from the line. Plug it in and you have

y=mx+ b

20=m(0) +b

b=20

Now we need another data point to find m which we already have. If you remember from part 1 x= 5 hrs there are y = 9 gallons left, thus another point from the line is (5, 9).

Now lets plug the values into y = mx + b and find m (which we already kind of found in part one)

y=mx+ b

9=m5+20

m5=(9-20)

m5=-11

m-=-11/5

Equation:

y=-11/5x+20

Hope this helps!