Question

With 51 gallons of fuel in its tank, the airplane has a weight of 2390.7 pounds. What is the weight of the plane with 81 gallons of fuel in its tank? The slope is 5.7

Answer 1

Answer: 2561.7 pounds

Step-by-step explanation:

If we assume the total weight of an airplane (in pounds units) as a linear function of the amount of fuel in its tank (in gallons) and we make a Weight vs amount of fuel graph, which resulting slope is 5.7, we can use the slope equation of the line:

`m=(Y-Y_(1))/(X-X_(1))` (1)

Where:

`m=5.7` is the slope of the line

`Y_(1)=2390.7pounds` is the airplane weight with 51 gallons of fuel in its tank (assuming we chose the Y axis for the airplane weight in the graph)

`X_(1)=51gallons` is the fuel in airplane's tank for a total weigth of 2390.7 pounds (assuming we chose the X axis for the a,ount of fuel in the tank in the graph)

This means we already have one point of the graph, which coordinate is:

`(X_(1),Y_(1))=(51,2390.7)`

Rewritting (1):

`Y=m(X-X_(1))+Y_(1)` (2)

As Y is a function of X:

`Y=f_((X))=m(X-X_(1))+Y_(1)` (3)

Substituting the known values:

`f_((X))=5.7(X-51)+2390.7` (4)

`f_((X))=5.7X-290.7+2390.7` (5)

`f_((X))=5.7X+2100` (6)

Now, evaluating this function when X=81 (talking about the 81 gallons of fuel in the tank):

`f_((81))=5.7(81)+2100` (7)

`f_((81))=2561.7` (8) This means the weight of the plane when it has 81 gallons of fuel in its tank is 2561.7 pounds.