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Let's work through this problem step by step:

You are given:
- A 20,000 gallon swimming pool.
- The pool currently contains 5,000 gallons of water.
- A hose fills the pool at a rate of 1,250 gallons per hour.

To model this situation mathematically, we can write an equation for the volume of water in the pool, \( V(t) \), as a function of time, \( t \) (in hours).

### Key information:
- Initial amount of water: 5,000 gallons
- Fill rate: 1,250 gallons per hour
- Maximum capacity: 20,000 gallons

The equation that represents the volume of water in the pool after \( t \) hours is:
\[
V(t) = 5000 + 1250t
\]
where \( V(t) \) is the total amount of water (in gallons) in the pool after \( t \) hours.

### Determine the time to fill the pool:
We need to determine how long it takes to fill the pool completely. Set \( V(t) = 20,000 \) and solve for \( t \):
\[
20000 = 5000 + 1250t
\]
\[
15000 = 1250t
\]
\[
t = \frac{15000}{1250} = 12 \text{ hours}
\]
So, it will take 12 hours to fill the pool.

### Plotting the graph:
- The starting point on the graph is at \( (0, 5000) \), where \( t = 0 \) hours and the pool has 5,000 gallons of water.
- The endpoint is at \( (12, 20000) \), where after 12 hours, the pool reaches its full capacity of 20,000 gallons.
  
On the graph, draw a straight line connecting these two points, which represents the linear relationship between time and the volume of water being added to the pool.

Would you like a more detailed explanation on plotting the graph, or do you need assistance with any other aspect of the problem?

### Follow-up questions:
1. What is the formula for the volume of water after \( t \) hours?
2. How long would it take to fill half of the pool starting from 5,000 gallons?
3. How would the graph change if the hose added water at 1,500 gallons per hour instead?
4. How much water is in the pool after 6 hours?
5. What would the graph look like if the pool initially contained 0 gallons of water?

### Tip:
When plotting a graph, always start by identifying key points such as the initial value and the endpoint, then use these to guide your graphing.

A 20,000 gallon swimming pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1250 gallons per hour. Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.

Learn how to plot a graph showing the water volume in a 20,000-gallon pool being filled from 5,000 gallons at a rate of 1,250 gallons per hour. Understand linear functions and rates of change with a detailed solution and graphing example. Suitable for Grades 8-10 students.

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