There are 3 different types of containers being tested as rain water storage devices. The depth of water in the 3 containers is graphed as a function of the number of days.

Find the container that shows a linear relationship between time and depth.

To identify the container that shows a **linear relationship** between time and the depth of water, you need to analyze the graphs of the three containers.

A **linear relationship** between two variables means that as one variable changes, the other changes at a constant rate. In the case of time and water depth, this would appear as a straight line on a graph. The key features of a linear relationship include:

- The graph forms a straight line (no curves or bends).
- The rate of change (slope) is constant.
- The equation of the graph can be written in the form \( y = mx + b \), where \( y \) represents the water depth, \( x \) represents time (days), \( m \) is the rate of change (slope), and \( b \) is the y-intercept.

### Steps to identify:
1. Look at the graph of each container.
2. Check if any of the graphs show a straight line with constant slope (indicating a consistent increase or decrease in water depth).
3. The container with the straight-line graph is the one with a linear relationship.

If you have the graphs available, you can upload them, and I can help you pinpoint which one shows this linear relationship.

Would you like to upload the graphs or proceed further with an explanation?

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Here are 5 related questions for further exploration:
1. What is the equation of a line that represents the depth of water over time for the linear container?
2. How can you calculate the slope of the linear relationship from the graph?
3. Can the water depth decrease over time in a linear relationship, and how would that appear on the graph?
4. What happens if the relationship between time and water depth is quadratic instead of linear?
5. How does the rate of water collection affect the steepness of the line in a linear graph?

**Tip:** A linear graph will always exhibit a constant rate of change, so the line’s steepness (slope) should remain the same at all points.

There are 3 different types of containers being tested as rain water storage devices. The depth of water in the 3 containers is graphed as a function of the number of days. Find the container that shows a linear relationship between time and depth.

Learn how to identify which container shows a linear relationship between time and water depth by analyzing the graphs of water storage in three containers. This solution explores linear relationships, the slope formula, and how to recognize a constant rate of change. Suitable for students in Grades 8-10.

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