Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank.

Question

When graphed, the function gives a line with a slope of 5.9. See the figure below. With 48 gallons of fuel in its tank, the airplane has a weight of 2383.2

pounds. What is the weight of the plane with 16

 gallons of fuel in its tank?

Answer 1

Here you need a bit of algebra to describe the function:

Linear function (straight line) of total amount of fuel.

Hence Weight_F = W₀ + 5.9G

where Weight_F = weight with fuel, W₀ = empty weight, G = gallons

And we know that 2383.2 = W₀ + 5.9(48)

hence, W₀ = 2383.2 - 5.9(48) = 2100 (2,100 llbs empty weight)

So our required equation is: Weight_F = 2100 + 5.9G

And finally, what is weight with 16 gallons?

Weight_F = 2100 + 5.9(16) = 2,194.4 gallons (rounded down to nearest gallon 2,194)

Answer 2

a line is y=mx+b

y = weight of the airplane

m = 5.9

x = gallons of fuel

b= ?

if the total weight is 2383.2 when there are 48 gallons of fuels:

2383.2 = 5.9(48)+b

2383.2 = 283.2+b

2100 = b

so the equation would be:

y = 5.9x+2100

now when x = 16 solve y = 5.9x+2100 simplify:

y=5.9(16)+2100