To determine the slope of the graph, we need to calculate the rate of change, which is $\frac{\Delta g}{\Delta t}$, where:

• $\Delta g$ is the change in gallons of water,
• $\Delta t$ is the change in time.

From the graph:

• At $t = 0$, $g = 0$ (starting point).
• At $t = 20$, $g = 100$ (endpoint).

The slope is calculated as: $\text{slope} = \frac{\Delta g}{\Delta t} = \frac{100 - 0}{20 - 0} = \frac{100}{20} = 5$

Answer:

The slope is 5 gallons per minute.

Would you like a detailed explanation of this calculation or related questions?

Here are 5 related questions:

1. What does the slope represent in the context of this problem?
2. How would the graph look if the slope was 3 gallons per minute instead of 5?
3. If the tank capacity is 200 gallons, how much time would it take to fill it at this rate?
4. What is the equation of the line representing the water filling the tank?
5. How would the graph change if the tank starts with 10 gallons instead of being empty?

Tip: The slope of a graph represents how quickly or slowly the dependent variable (e.g., gallons) changes with respect to the independent variable (e.g., time).