https://file.aiquickdraw.com/mathbot/file/17286310971548cx4qhgs.jpg

Let's analyze the problem based on the graph and questions provided:

### (a) What is the amount of water in the tank at 0 minutes?
From the graph, it looks like the amount of water in the tank at time \( t = 0 \) is about **50 liters**. This is based on the y-intercept of the graph, which represents the initial amount of water in the tank when no time has passed.

### (b) Rate of Change of Water in the Tank
The second part of the question asks about the relationship between time and the amount of water in the tank.

- **The amount of water is increasing as time increases**. You can tell this because the line on the graph is going upwards, indicating a positive slope.
- To determine the rate at which the amount of water is increasing, we need to find the **slope** of the line. The slope can be calculated using two points on the line, such as:
  - Point 1: \( (0 \text{ minutes}, 50 \text{ liters}) \)
  - Point 2: \( (6 \text{ minutes}, 350 \text{ liters}) \)

The formula for the slope \( m \) is:
\[
m = \frac{{\text{Change in amount of water}}}{{\text{Change in time}}} = \frac{350 - 50}{6 - 0} = \frac{300}{6} = 50 \, \text{liters per minute}
\]

So, the water is increasing at a rate of **50 liters per minute**.

### Final Answers:
- **(a)**: 50 liters
- **(b)**: The amount of water increases at a rate of **50 liters per minute**.

Would you like more details on any part of this problem?

Here are five related questions to expand on this:
1. How would the graph change if the rate of filling the tank decreased?
2. What would the equation of the line be for this scenario?
3. How can we calculate the total amount of water after a given period, such as 10 minutes?
4. What does the slope of the graph represent in practical terms?
5. How would you adjust the graph if there was an initial amount of 100 liters in the tank?

**Tip**: Always check the slope of a line when determining the rate of change in real-world problems like this. It tells you how fast something is changing over time.

Latoya is filling a tank. The graph shows the amount of water (in liters) in the tank versus time (in minutes). What is the amount of water in the tank at 0 minutes? At what rate is the amount of water increasing?

Learn how to analyze a graph showing the relationship between time and the amount of water in a tank. This problem involves calculating the slope (rate of change) and determining the initial amount of water. Suitable for students in Grades 6-8.

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