Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 12 gallons of fuel, the airplane weighs 2078 pounds. When carrying 40 gallons of fuel, it weighs 2260 pounds. How much does the airplane weigh if it is carrying 54 gallons of fuel?

GIVEN: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying [tex]12[/tex] gallons of fuel, the airplane weighs [tex]2078[/tex] pounds. When carrying [tex]40[/tex] gallons of fuel, it weighs [tex]2260[/tex] pounds.

TO FIND: How much does the airplane weigh if it is carrying [tex]54[/tex] gallons of fuel.

SOLUTION:

Let the fuel be represented along [tex]\text{x-axis}[/tex] and weight of plane along [tex]\text{y-axis}[/tex]

two coordinates are [tex](12,2078)\text{ and }(40,2260)[/tex]

now, equation of linear function is

[tex]\text{y}-\text{y}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}(\text{x}-\text{x}_1)[/tex]

putting values we get

[tex]\text{y}-2078=\frac{182}{28}(\text{x}-12)[/tex]

[tex]2\text{y}=13\text{x}+4000[/tex]

Now when fuel is [tex]54\text{ gallons}[/tex]

[tex]2\text{y}=13\times54+4000[/tex]

[tex]\text{y}=2351\text{ pounds}[/tex]

Airplane weighs [tex]2351\text{ pounds}[/tex]