https://file.aiquickdraw.com/mathbot/file/172662511521259gzarme.jpg

To answer the question based on the provided graph:

The position-time graph shows two lines, one representing Sarah's motion (blue line) and the other representing Michael's motion (orange line). In a position-time graph, the slope of the line represents the velocity (speed) of each person.

- Sarah's line has a steeper slope compared to Michael's, meaning her position increases more rapidly over time.
- A steeper slope indicates a higher speed.

### Conclusion:
- **Option (a): "Sarah is walking faster than Michael"** is the correct answer because Sarah's line has a steeper slope, meaning she is moving faster than Michael.

Let me know if you need more details or explanations.

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### Follow-up Questions:
1. What is the significance of the slope in a position-time graph?
2. How can we calculate the exact speeds of Sarah and Michael from this graph?
3. Can two objects have different velocities but the same starting point in a position-time graph?
4. How would a graph look if someone were to stop walking for a while?
5. What would the graph look like if Sarah or Michael reversed direction?

**Tip:** In position-time graphs, a steeper line always indicates a higher speed.

Sarah and Michael are walking along a straight track. Their motions are represented by the position-time graph below. Which of the following statements about their motion are true? a) Sarah is walking faster than Michael b) Michael is walking faster than Sarah c) Sarah and Michael are walking at the same speed d) Sarah and Michael are walking in opposite directions

Understand how to interpret position-time graphs to compare speeds. Learn why Sarah is walking faster than Michael using the slope concept. Suitable for middle school students in Grades 6-8.

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