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 6.0. See the figure below.
With 50 gallons of fuel in its tank, the airplane has a weight of 2,400 pounds. What is the weight of the plane with 78 gallons of fuel in its tank?

We are given that the weight of the airplane \( W \) is a linear function of the amount of fuel \( F \) in its tank. From the information provided:

- The slope of the line is 6.0. This means that for every additional gallon of fuel, the weight increases by 6 pounds.
- When the plane has 50 gallons of fuel, its weight is 2,400 pounds.

The equation of a line can be written as:

\[
W = mF + b
\]

where:
- \( W \) is the weight of the airplane,
- \( F \) is the amount of fuel in gallons,
- \( m \) is the slope of the line (6 pounds per gallon),
- \( b \) is the y-intercept, representing the weight of the airplane with no fuel.

### Step 1: Find the y-intercept (\( b \))
We know that with 50 gallons of fuel, the weight is 2,400 pounds. Substituting \( W = 2400 \), \( F = 50 \), and \( m = 6 \) into the equation:

\[
2400 = 6(50) + b
\]

\[
2400 = 300 + b
\]

\[
b = 2400 - 300 = 2100
\]

Thus, the equation of the line is:

\[
W = 6F + 2100
\]

### Step

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 6.0. With 50 gallons of fuel in its tank, the airplane has a weight of 2,400 pounds. What is the weight of the plane with 78 gallons of fuel in its tank?

Solve the problem of calculating an airplane's weight based on a linear function of the fuel amount. With a slope of 6.0, find the airplane's weight when it has 78 gallons of fuel, using the equation W = 6F + 2100. Suitable for students in Grades 8-10.

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