https://file.aiquickdraw.com/mathbot/file/1728587393612fbunoy2q.jpg

Let's analyze the problem step by step to determine which graph represents Marc's drive to work.

1. **Start:**
   - Marc pulls out of his driveway slowly at a constant speed, then **comes to a stop** at the stop sign at the end of the street. This indicates an increase in speed followed by a stop (speed goes to zero).
   
2. **Waiting at the stop sign:**
   - Marc waits at the stop sign until it is his turn, meaning his speed remains **zero for some time**.

3. **After stop sign:**
   - His speed **increases steadily** until he reaches the speed limit, meaning a gradual rise in speed.

4. **Driving at a constant speed:**
   - He then drives at a **constant speed** until he approaches the office.

5. **Slowing down and stopping:**
   - Near the office, Marc slows down and comes to a **complete stop** in front of his office.

### Key features to look for in the graph:
- **Gradual increase in speed** (pulling out of the driveway).
- **Complete stop** (at the stop sign).
- **Period of zero speed** (waiting at the stop sign).
- **Gradual increase in speed** (after leaving the stop sign).
- **Constant speed** (driving to the office).
- **Gradual decrease to zero speed** (slowing down in front of the office).

#### The graph that matches this description is the **bottom left graph**:
- It shows an initial rise in speed followed by a stop, a steady increase after the stop sign, constant speed, and finally a gradual decrease to zero.

Would you like further details or explanation on this? 

### Follow-up Questions:
1. What would happen if Marc didn't stop at the stop sign?
2. How would the graph look if Marc sped up much faster after the stop sign?
3. How can we model Marc's acceleration mathematically?
4. What would the graph look like if Marc encountered traffic before reaching the office?
5. How would the graph change if Marc decelerated more gradually before stopping at his office?

### Tip:
When analyzing speed-time graphs, the slope of the line represents acceleration, and flat sections represent constant speed.

Marc left his house to drive to work. He slowly pulls out of his driveway at a constant speed and continues at that speed until he slows and comes to a complete stop at the stop sign at the end of his street. He waits at the stop sign until it is his turn to go, and then his speed steadily increases until he reaches the speed limit. He drives at this constant speed until he approaches the office. He slows down steadily and comes to a complete stop in front of his office. Which graph represents Marc's drive to work?

This problem focuses on interpreting a speed-time graph for Marc's drive to work. Key concepts include constant speed, acceleration, and interpreting speed changes over time. Suitable for middle school students in Grades 6-8.

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