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

Question

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
10
gallons of fuel, the airplane weighs
2058
pounds. When carrying
45
gallons of fuel, it weighs
2261
pounds. How much does the airplane weigh if it is carrying
60
gallons of fuel?

Answer 1

The question says that there is a linear relationship between the weight of an airplane and the amount of fuel in its tank. To solve this equation, we can put the information in slope-intercept form. Y is a function of X. In our example, Y is the weight of the airplane. X is the amount of fuel in its tank. First, let’s start by finding “m”, the slope of the line. m = (difference of the y’s) / (difference of the x’s). m = (2261-2058)/(45-10) = 5.8

Then plug that back into the equation with one set of coordinates. y = 5.8x + b

2058 = 5.8*10 + b

2058 = 58 + b

2058 - 58 = b

2000 = b

Now you have “b”, the y-intercept. So what is your equation in slope intercept form? y = 5.8x + 2000

you can use this to find the weight of a plane carrying 60 gallons of fuel. You plug 60 into x and find y.

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