SOLUTION: A driver notices that after driving 100 miles there are 12.8 gallons of fuel left in her car's tank. After driving 300 miles she notices that there are only 6.4 gallons left in th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A driver notices that after driving 100 miles there are 12.8 gallons of fuel left in her car's tank. After driving 300 miles she notices that there are only 6.4 gallons left in th      Log On


   

Question 198309: A driver notices that after driving 100 miles there are 12.8 gallons of fuel left in her car's tank. After driving 300 miles she notices that there are only 6.4 gallons left in the tank.
A) Determine a linear function that will give the number of gallons left in the tank as a function of the number of miles driven.
B)Based on this model how much fuel does the tank hold?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A driver notices that after driving 100 miles there are 12.8 gallons of fuel left in her car's tank. After driving 300 miles she notices that there are only 6.4 gallons left in the tank.
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You have two points: (12.8,100), (6.4,300)
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A) Determine a linear function that will give the number of gallons left in the tank as a function of the number of miles driven.
slope = (300-100)/(6.4-12.8) = 200/-6.4 = -31.25
intercept: 100 = -31.25*12.8 + b
b = 500
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Equation:
GL(m) = -31.25m + 500
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B)Based on this model how much fuel does the tank hold?
If the miles = 0 the Gas Left is 500 gallons
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Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st step is to decide what goes on the x-axis
and what goes on the y-axis.
Q: Does miles driven determine how much is left
in the tank?
Does how much is left in the tank determine the
miles?
The 1st statement is true, so y-axis is the gallons
left in tank and x-axis is the miles driven
(x causes y)
I'm given 2 points, (x,y):
(100,12.8)
(300,6.4)
The formula is:
%28y+-+6.4%29%2F%28x+-+300%29+=+%2812.8+-+6.4%29%2F%28100+-+300%29
%28y+-+6.4%29%2F%28x+-+300%29+=+6.4%2F-200
Multiply both sides by -200%2A%28x+-+300%29
%28y+-+6.4%29%2A%28-200%29+=+6.4%2A%28x+-+300%29
-200y+%2B+1280+=+6.4x+-+1920
200y+=+-6.4x+%2B+3200
y+=+-.032x+%2B+16
I checked the points (100,12.8) and (300,6.4)
They are on this line
Here's a plot:
+graph%28+400%2C+400%2C+-50%2C+550%2C+-2%2C+20%2C+-.032x+%2B+16%29+
If the driver drives 0 miles (uses no gas), there are
16 gallons in the tank (full)
y+=+-.032%2A0+%2B+16
y+=+16