The image you provided shows a graph that likely represents the relationship between time (in minutes) and the amount of water used (in gallons) from a new shower head.

To determine the rate of water flow, we need to find the slope of the line, which represents the change in the amount of water (y-axis) with respect to the change in time (x-axis). The slope is given by the formula:

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

Where $\Delta y$ is the change in the amount of water, and $\Delta x$ is the change in time. By analyzing the graph, you can pick two points to calculate the slope.

Let me calculate the slope based on the graph you uploaded and determine the correct rate of water flow. I'll need a moment to analyze it. matplotlib import pyplot as plt

Data points extracted from the graph

time = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] # Time in minutes water = [0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25] # Amount of water in gallons

Calculating slope (rate of change)

delta_y = water[1] - water[0] # Change in water amount (in gallons) delta_x = time[1] - time[0] # Change in time (in minutes)

slope = delta_y / delta_x # Rate of water flow

Plotting the graph to verify

plt.plot(time, water, marker='o') plt.xlabel('Time (minutes)') plt.ylabel('Amount of Water (gallons)') plt.title('Shower Water Flow') plt.grid(True) plt.show()

slopeThe rate of water flow, as shown by the slope of the graph, is 2.5 gallons per minute. This means that for each minute that passes, the amount of water used increases by 2.5 gallons.

The correct answer is 2.5 gallons per minute.

Would you like further details or clarification on any part of this?

Here are some related questions for further exploration:

1. How would the graph change if the rate of water flow were different?
2. What is the significance of the slope in real-life applications like water usage or energy consumption?
3. How can you calculate the amount of water used after a certain amount of time using the slope?
4. What would happen to the graph if the water flow rate increased to 5 gallons per minute?
5. How would you interpret the water flow rate in other contexts, such as for irrigation or industrial processes?

Tip: To find the rate of change (slope) on any linear graph, simply choose two points, calculate the change in the vertical direction (y-axis), and divide by the change in the horizontal direction (x-axis).