Question

Application problem with a linear function: Finding a coordinate...Madison vSuppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 25 gallons of fuel, theairplane weighs 2145 pounds. When carrying 40 gallons of fuel, it weighs 2232 pounds. How much does the airplane weigh if it is carrying 50 gallons of fuel?

Answer 1

Linear function

y=mx+c

let x be the gallon

let y be the airplane weight

where is m is the slope

from the given information

`\begin{gathered} (x_1,y_1)=(25,2145) \\ (x_{2,_{}}y_2)=(40,2232) \\ M\text{ =}\frac{y_2-y_1_{}}{x_2-x_1} \\ M=(2232-2145)/(40-25) \\ M=(87)/(15) \\ M=5.8 \end{gathered}`

`\begin{gathered} y-y_1=m(x-x_1) \\ y-2145=5.8(x-25) \\ y-2145=5.8x-145 \\ y=5.8x-145+2145 \\ y=5.8x+2000 \\ \text{From the equation x=50} \\ y=5.8(50)+2000 \\ y=290+2000 \\ y=2290\text{ pounds} \end{gathered}`