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

Question

When carrying 16 gallons of fuel, the airplane weighs 1988

 pounds. When carrying 50 gallons of fuel, it weighs 2175

 pounds. How much does the airplane weigh if it is carrying 66 gallons of fuel?

Answer 1

You need to first write the linear equation relating the number of gallons of fuel to the weight of the aircraft as:

y = mx + b, where x is the number of gallons and y is the weight of the aircraft in pounds.

now, we can use the two sets of data points given to us to first solve for the slope m as:

m = (2175 - 1988)/(50 - 16) = 5.5. Therefor, we can now write:

y - y0 = m(x - x0) or y - 1988 = 5.5(x - 16) giving us y = 5.5x + 1900.

With this equation of the line, we just need to put the desired number of gallons as x and solve for the weight of the aircraft, y.

y = 5.5*66 + 1900 = 2263 pounds.

Answer 2

(16,1988)

(50,2175)

slope is (2175-1988)/(50-16)

= 187/34

= 5.5

B = y - mx

= 2175 - 5.5(50)

= 2175 - 275

= 1900

y = 5.5x+1900 = f(x)

f(66) = 2263