SOLUTION: Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope o

Algebra ->  Points-lines-and-rays -> SOLUTION: Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope o      Log On


   

Question 293909: Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 5.7.
With 47 gallons of fuel in its tank, the airplane has a weight of 2367.9 pounds. What is the weight of the plane with 20 gallons of fuel in its tank?

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You could start with the slope-intercept form of a linear equation:W+=+mF%2Bb where: W = weight of plane and F = amount of fuel in gallons.
The slope, m, of the function is given as: m+=+5.7 so you can substitute.
W+=+5.7F%2Bb You can find b, the W-intercept (or the weight of the plane with no fuel) by substituting the given fuel and weight amounts: W = 2367.9 and F = 47.
2367.9+=+5.7%2847%29%2Bb
b+=+2100 so the final equation is:
W+=+5.7F%2B2100 Now you can find the weight, W, of the plane when it has 20 gallons of fuel (F=20) in its tank.
W+=+5.7F%2B2100 Substitute F = 20.
W+=+5.7%2820%29%2B2100
highlight%28W+=+2214%29lbs.