Question
Franco lives in the desert and is concerned about his water consumption. He's curious how much water he uses when he showers. There is a linear relationship between the time, in minutes, Franco spends in the shower, and the amount of water he uses, in gallons. 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 x y Time (minutes) Water used (gallons) Describe the rate of change for this relationship. The amount of water Franco uses increases decreases by 2 9 of a gallon 4 9 of a gallon 2 1 4 gallons 4 1 2 gallons 8gallons 18gallons per minute.
Answers
GPT-4o mini
To describe the rate of change for Franco's water consumption based on the time he spends in the shower, we need to analyze the relationship you've provided. Since the relationship is linear and you provided values for time (x) and corresponding water use (y), we can determine the slope, which represents the rate of change.
1. **Understanding the data:**
- Let's assume the pairs of time (in minutes) and water used (in gallons) you listed are consistent:
For example, we might interpret them as:
- 2 minutes -> 2 gallons
- 4 minutes -> 4 gallons
- 6 minutes -> 6 gallons
- ...
- 20 minutes -> 20 gallons
2. **Identifying the relationship:**
- It seems that for every increase of 2 minutes in shower time, the water usage also increases by 2 gallons.
3. **Calculating the rate of change:**
- The rate of change (slope) can be calculated by taking the change in gallons divided by the change in minutes.
- Based on the pattern:
\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{2 \text{ gallons}}{2 \text{ minutes}} = 1 \text{ gallon per minute}
\]
4. **Final Conclusion:**
- Thus, the amount of water Franco uses increases by **1 gallon per minute**.
From the options you provided, it looks like none directly match the rate of 1 gallon per minute, but that is the accurate description of the rate of change for your given relationship. Please verify the data points to see if there might be a misunderstanding in the values presented.
1. **Understanding the data:**
- Let's assume the pairs of time (in minutes) and water used (in gallons) you listed are consistent:
For example, we might interpret them as:
- 2 minutes -> 2 gallons
- 4 minutes -> 4 gallons
- 6 minutes -> 6 gallons
- ...
- 20 minutes -> 20 gallons
2. **Identifying the relationship:**
- It seems that for every increase of 2 minutes in shower time, the water usage also increases by 2 gallons.
3. **Calculating the rate of change:**
- The rate of change (slope) can be calculated by taking the change in gallons divided by the change in minutes.
- Based on the pattern:
\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{2 \text{ gallons}}{2 \text{ minutes}} = 1 \text{ gallon per minute}
\]
4. **Final Conclusion:**
- Thus, the amount of water Franco uses increases by **1 gallon per minute**.
From the options you provided, it looks like none directly match the rate of 1 gallon per minute, but that is the accurate description of the rate of change for your given relationship. Please verify the data points to see if there might be a misunderstanding in the values presented.