The problem states:

• Context: Owners of a recreation area are filling a small pond with water.
• Water flow rate: 35 liters per minute.
• Initial water amount: 600 liters already in the pond.

Let $W$ represent the amount of water in the pond in liters, and let $T$ represent the number of minutes since they started adding water.

Step-by-Step Solution:

1. Identify the form of the equation: Since water is added at a constant rate, the equation will be in the form: $W = \text{(initial amount)} + \text{(rate)} \times T$

2. Plug in the values:

   • Initial amount of water = 600 liters
   • Rate of water flow = 35 liters per minute

   So the equation becomes: $W = 600 + 35T$

3. Graphing the equation:

   • This equation represents a straight line with a y-intercept of 600 (when $T = 0$, $W = 600$) and a slope of 35.
   • To graph, plot the y-intercept at (0, 600) and use the slope to determine other points (e.g., at $T = 1$, $W = 635$).

Final Answer:

The equation relating $W$ to $T$ is: $W = 600 + 35T$

Would you like details on graphing this equation or have any other questions?

Related Questions to Explore:

1. What would the equation look like if the initial amount of water was different?
2. How does changing the rate (liters per minute) affect the equation?
3. If they stop adding water after a certain time, how would the equation change?
4. How long would it take to fill the pond to 2000 liters using this rate?
5. What does the slope represent in real-world terms in this context?

Tip:

When modeling word problems, identify constant rates and initial values; these often define the linear relationship's slope and intercept.