Question

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?

Answer 1

2002 pounds

Step-by-step 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

`y-y_1=m(x-x_1)`

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:

`y-2206=6(x-51)`

Now, we can solve for y

`\begin{gathered} y-2206=6(x)-6(51) \\ y-2206=6x-306 \\ y=6x-306+2206 \\ y=6x+1900 \end{gathered}`

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