Question

Suppose that the weight in pounds of an airplane is a linear function of the amount of fuel in gallons and it’s tank. When carrying 16 gallons of fuel the airplane Waze 2188 pounds. When carrying 48 gallons of fuel it weighs 2364 pounds. How much does the airplane way if it is carrying 64 gallons of fuel.

Answer 1

Data:

• ( 16, 2188 )

,

• ( 48, 2364 )

,

• Linear function

$y=mx+b$

Procedure:

0. Building up the linear equation: finding the slope (,m,)

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{2364-2188}{48-16}$$m=\frac{11}{2}$

2. Finding the intersection with y-axis ( b ): choosing the first point given to replace the values in the linear function.

$y=mx+b$$2188=\frac{11}{2}\cdot16+b$$2188=88+b$$88+b=2188$$b=2188-88$$b=2100$

3. Obtaining the linear function of the given problem:

$y=\frac{11}{2}x+2100$

4. Finding the weight of the airplane when it is carrying 64 gallons of fuel.

$y=\frac{11}{2}\cdot64+2100$$y=2452$

Answer: 2452 pounds