GRAPHS AND FUNCTIONS
Application problem with a linear function: Finding a coordinate.
Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 6.3 . See the figure below.
With 47 gallons of fuel in its tank, the airplane has a weight of 2196.1 pounds. What is the weight of the plane with 79 gallons of fuel in its tank?

Step 1 ：We are given that the weight of the airplane is a linear function of the total amount of fuel in its tank. The slope of this function is 6.3. We also know that when the airplane has 47 gallons of fuel, it weighs 2196.1 pounds.

Step 2 ：We can use the point-slope form of a linear equation to find the equation of the line. The point-slope form of a linear equation is \(y - y1 = m(x - x1)\), where \(m\) is the slope and \((x1, y1)\) is a point on the line.

Step 3 ：Substituting the given values into the equation, we get \(y - 2196.1 = 6.3(x - 47)\).

Step 4 ：We can simplify this equation to find the weight of the plane when it has 79 gallons of fuel. Substituting \(x = 79\) into the equation, we get \(y = 6.3 * (79 - 47) + 2196.1\).

Step 5 ：Calculating the above expression, we find that the weight of the plane with 79 gallons of fuel in its tank is 2397.7 pounds.

Step 6 ：\(\boxed{2397.7}\) pounds is the final answer.