Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 600 liters in the pond to start. Let *W* represent the amount of water in the pond (in liters), and let *T* represent the number of minutes that water has been added. Write an equation relating *W* to *T*, and then graph your equation.


To formulate an equation relating the amount of water \(W\) in the pond to the time \(T\) in minutes, we start by considering the initial amount of water and the rate at which water is being added.

Given:
- Initial amount of water in the pond: 600 liters
- Rate of adding water: 35 liters per minute

Let:
- \(W\) be the total amount of water in the pond (in liters)
- \(T\) be the time in minutes that water has been added

### Step 1: Formulate the equation
The amount of water in the pond after \(T\) minutes can be found by adding the initial amount of water to the product of the rate of adding water and the time.

\[ W = 600 + 35T \]

This is the linear equation relating \(W\) to \(T\).

### Step 2: Graph the equation

To graph the equation \(W = 600 + 35T\):

1. **Determine the intercepts**:
   - The initial amount of water (when \(T = 0\)): \(W = 600\)
   - This gives us the point \((0, 600)\).

2. **Choose another point**:
   - For example, after 10 minutes (\(T = 10\)):
     \[ W = 600 + 35 \times 10 = 600 + 350 = 950 \]
   - This gives us the point \((10, 950)\).

3. **Plot the points and draw the line**:
   - Plot the points \((0, 600)\) and \((10, 950)\) on the graph.
   - Draw a straight line passing through these points.

Below is a sketch of the graph based on these points:

\[
\begin{array}{c|c}
\text{T (minutes)} & \text{W (liters)} \\
\hline
0 & 600 \\
10 & 950 \\
20 & 1300 \\
30 & 1650 \\
\end{array}
\]

Using these points, you can graph the linear equation on a coordinate plane.

Would you like more details or have any questions about this problem?

Here are 8 relative questions that expand on this topic:
1. How would the equation change if the initial amount of water were different?
2. How do you determine the slope of the line from the equation \(W = 600 + 35T\)?
3. What is the significance of the y-intercept in this context?
4. How long will it take to fill the pond with 2000 liters of water?
5. What is the graphical representation if the rate of adding water changes to 50 liters per minute?
6. How can you represent this problem using a table of values?
7. What other real-life situations can be modeled using a similar linear equation?
8. How would you calculate the total amount of water added after a given time period?

**Tip:** When graphing a linear equation, it's helpful to calculate and plot multiple points to ensure accuracy in drawing the line.

Learn how to relate the amount of water in a pond (W) to the time (T) in minutes using a linear equation. Initial water amount is 600 liters, with water added at a rate of 35 liters per minute. Explore step-by-step solution, graphing the equation, and related questions. Suitable for students in Grades 7-9.

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