Choose the situation that best matches the graph of the function. Amount of Water in Tub (gallons) 20- 15- 10- S 0 1 2 3 -50 4 Time (minutes) 6 OA bathtub is filled at a constant rate of 1.75 gallons per minute. A bathtub is drained at a constant rate of 1.75 gallons per minute A bathtub contains 2.5 gallons of water. A bathtub is filled at a constant rote of 2.5 gallons per minute. FA 8 16

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Graph Analysis: Understanding Rate of Change**

In this problem, you are asked to choose the situation that best matches the graph of the function. 

### Graph Description
- **Axes:**
  - The x-axis represents **Time (minutes)**.
  - The y-axis represents **Amount of Water in Tub (gallons)**.
  
- **Graph Line:**
  - The line starts at the point (0, 20) on the y-axis and descends directly to the point (8, 0) on the x-axis, forming a straight line. This indicates a consistent rate of change.

### Options Provided
1. A bathtub is filled at a constant rate of 1.75 gallons per minute.
2. A bathtub is drained at a constant rate of 1.75 gallons per minute.
3. A bathtub contains 2.5 gallons of water.
4. A bathtub is filled at a constant rate of 2.5 gallons per minute.

### Graph Interpretation
- Since the line is descending from 20 gallons to 0 gallons over a period of 8 minutes, it indicates a draining action at a steady rate.
- The slope of the line represents the rate of change in the amount of water: a decline from 20 gallons to 0 gallons over 8 minutes is a rate of 2.5 gallons per minute.

**Correct Answer:**
- The bathtub is drained at a constant rate of 2.5 gallons per minute.

### Additional Note
Understanding the slope of the line helps in interpreting whether the situation described is a filling or draining process and at what rate. In this case, a negative slope indicates a decrease in the water level.
Transcribed Image Text:**Graph Analysis: Understanding Rate of Change** In this problem, you are asked to choose the situation that best matches the graph of the function. ### Graph Description - **Axes:** - The x-axis represents **Time (minutes)**. - The y-axis represents **Amount of Water in Tub (gallons)**. - **Graph Line:** - The line starts at the point (0, 20) on the y-axis and descends directly to the point (8, 0) on the x-axis, forming a straight line. This indicates a consistent rate of change. ### Options Provided 1. A bathtub is filled at a constant rate of 1.75 gallons per minute. 2. A bathtub is drained at a constant rate of 1.75 gallons per minute. 3. A bathtub contains 2.5 gallons of water. 4. A bathtub is filled at a constant rate of 2.5 gallons per minute. ### Graph Interpretation - Since the line is descending from 20 gallons to 0 gallons over a period of 8 minutes, it indicates a draining action at a steady rate. - The slope of the line represents the rate of change in the amount of water: a decline from 20 gallons to 0 gallons over 8 minutes is a rate of 2.5 gallons per minute. **Correct Answer:** - The bathtub is drained at a constant rate of 2.5 gallons per minute. ### Additional Note Understanding the slope of the line helps in interpreting whether the situation described is a filling or draining process and at what rate. In this case, a negative slope indicates a decrease in the water level.
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