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The image shows a problem related to a graph where a bucket is being filled with water. The graph plots the height of the water (in millimeters) versus time (in seconds). Two questions are asked based on the graph:

1. **(a)** What is the slope of the line?
2. **(b)** How much does the height of the water increase per second that water flows?

### Solution:

We will first analyze the graph and then proceed to answer each question.

#### (a) Slope of the line:

The slope (or "pendiente" in Spanish) of a straight line is calculated as:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\text{change in height}}{\text{change in time}}
\]

From the graph, we can choose two points:
- Point 1: \( (0 \text{ seconds}, 0 \text{ mm}) \)
- Point 2: \( (6 \text{ seconds}, 30 \text{ mm}) \)

Now, calculating the slope:

\[
\text{slope} = \frac{30 \text{ mm} - 0 \text{ mm}}{6 \text{ seconds} - 0 \text{ seconds}} = \frac{30 \text{ mm}}{6 \text{ seconds}} = 5 \text{ mm/second}
\]

So, the slope is **5 mm/second**.

#### (b) How much does the height of the water increase per second?

This question is asking for the same value as the slope because the slope represents how much the height increases for each second. Therefore, the height of the water increases by **5 mm per second**.

### Final Answers:
- (a) The slope is **5 mm/second**.
- (b) The height increases by **5 mm** each second.

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Would you like further explanation or details? 

Here are 5 related questions to explore more:

1. What is the meaning of the slope in a distance-time graph?
2. How would the graph look if the bucket filled up faster?
3. What would be the interpretation if the slope were negative?
4. How can you find the y-intercept from the graph?
5. How does the slope change if the flow of water slows down?

**Tip**: The slope of a line can always be interpreted as the rate of change of the y-value with respect to the x-value.

A bucket is being filled with water. The graph shows the height of the water (in mm) over time (in seconds). (a) What is the slope of the line? (b) How much does the height of the water increase per second that the water flows?

Solve a problem where a bucket fills with water, analyzing the height of the water over time. Calculate the slope of the line (rate of change) to determine how much the water height increases per second. This problem covers key concepts like slope calculation and rate of change.

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