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

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:

$m=\frac{Y-Y_{1}}{X-X_{1}}$  (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.