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The problem involves a linear relationship between the weight of an airplane and the amount of fuel in its tank. Let's break this down step by step:

### Given Information:
- The relationship is linear, which means we can use the formula for a line:  
  \[
  y = mx + b
  \]
  where:
  - \(y\) is the weight of the airplane (in pounds),
  - \(x\) is the amount of fuel (in gallons),
  - \(m\) is the slope (rate of change of weight with fuel),
  - \(b\) is the y-intercept (weight of the airplane without fuel).
  
- The **slope** of the line is given as \(6.1\).
- With **46 gallons of fuel**, the airplane's weight is **2380.6 pounds**.
- We need to find the weight of the airplane with **19 gallons of fuel**.

### Step-by-Step Solution:

1. **Forming the Equation**:
   From the point \((46, 2380.6)\) and the slope \(6.1\), we can plug this into the equation \(y = mx + b\) to find the y-intercept \(b\).
   \[
   2380.6 = 6.1(46) + b
   \]
   Let's solve for \(b\).

2. **Calculate the Weight with 19 Gallons**:
   After finding \(b\), we can use the equation to calculate the weight when \(x = 19\) gallons.

Let me calculate this.The weight of the airplane with 19 gallons of fuel in its tank is **2215.9 pounds**.

Would you like further details on how this was calculated, or do you have any other questions?

Here are five related questions you might find helpful:
1. How would the equation change if the slope were different?
2. What does the slope represent in this context?
3. How do we interpret the y-intercept in a real-world scenario?
4. If the fuel tank was empty, how much would the airplane weigh?
5. How would you find the amount of fuel if given the airplane's weight?

**Tip**: In linear equations, the slope represents the rate of change, which in this case is the increase in weight per gallon of fuel.

With 46 gallons of fuel in its tank, the airplane has a weight of 2380.6 pounds. What is the weight of the plane with 19 gallons of fuel in its tank?

Learn how to calculate the weight of an airplane with 19 gallons of fuel using the linear equation y = mx + b. The problem involves a slope of 6.1 and a given weight of 2380.6 pounds with 46 gallons of fuel. Suitable for Grades 8-10.

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