Respuesta :
Since the weight and fuel have a linear relation, we can write it as
[tex]y=mx+b[/tex]where y denotes the weight in pounds and x the fuel in gallons.
We have 2 points of this linear relation, they are
[tex]\begin{gathered} (x_1,y_1)=(10,1955) \\ \text{and} \\ (x_2,y_2)=(38,2109) \end{gathered}[/tex]so the slope m from above is given as
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2109-1955}{38-10} \end{gathered}[/tex]which gives
[tex]\begin{gathered} m=\frac{154}{28} \\ m=5.5 \end{gathered}[/tex]Then, the line equation has the form
[tex]y=5.5x+b[/tex]Now, we can find the y-intercept b by replacing one of the two given points, that is, if we substitute point (10,1955) into the last result, we get
[tex]1955=5.5(10)+b[/tex]then, b is obtained as
[tex]\begin{gathered} 1955=55+b \\ b=1955-55 \\ b=1900 \end{gathered}[/tex]So, the line equation which model this problem is
[tex]y=5.5x+1900[/tex]Hence, by using this equation, we can find the weight of the airplane when the fuel is equal to 56 gallons, that is,
[tex]y=5.5(56)+1900[/tex]which gives
[tex]\begin{gathered} y=308+1900 \\ y=1938 \end{gathered}[/tex]How much does the airplane weight if it’s carrying 56 gallons of fuel? 1938 pounds
