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Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tahk. When graphed, the function gives a linewith a slope of 6.0. See the figure below.With 51 gallons of fuel in its tank,the airplane has a weight of 2206 pounds. What is the weight of the plane with 17 gallons of fuel in its tank?

Respuesta :

Answer:

2002 pounds

Explanation:

To know the weight of the plane, we need to find an equation that relates the amount of fuel to the weight.

This equation can be founded using the following

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope, x1 is the number of gallons and y1 is the respective weight. So, replacing m = 6.0, x1 = 51 gallons and y1 = 2206 pounds, we get:

[tex]y-2206=6(x-51)[/tex]

Now, we can solve for y

[tex]\begin{gathered} y-2206=6(x)-6(51) \\ y-2206=6x-306 \\ y=6x-306+2206 \\ y=6x+1900 \end{gathered}[/tex]

Then, we can calculate the weight of an airplane with 17 gallons of fuel replacing x = 17 on the equation above

y = 6x + 1900

y = 6(17) + 1900

y = 102 + 1900

y = 2002

Therefore, the answer is 2002 pounds

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