To find the rate at which the pool is being filled (i.e., gallons per minute), we need to calculate the slope of the line on the graph, which represents the relationship between the volume of water (y) and time (x). The slope of the line is given by the formula:

$\text{slope} = \frac{\Delta y}{\Delta x}$

Where:

• $\Delta y$ is the change in the volume of water (gallons),
• $\Delta x$ is the change in time (minutes).

Steps:

1. Identify two points $(x_1, y_1)$ and $(x_2, y_2)$ from the graph, which give the number of gallons in the pool at specific times.
2. Apply the slope formula to calculate the rate at which the pool is being filled.

If you provide the graph or the specific points from it, I can calculate the exact rate of filling (gallons per minute).

Would you like to upload the graph, or provide the coordinates?

Related Questions:

1. How does the slope of a graph relate to rate in different contexts?
2. How can we calculate the total volume of the pool using this rate and the time taken to fill it?
3. What does a steeper slope on the graph signify in terms of pool filling?
4. How can we find the time it will take to fill the pool completely?
5. How can we modify the rate of filling (gallons per minute) in a real-world situation?

Tip: The slope of a line on a graph can always be interpreted as a rate of change in the context of the variables being compared.