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The graph shows the number of cars in the parking lot of a major retailer (in hundreds) in the hours after midnight.  

What is true about this graph?The number of cars at 10 am is decreasing faster than the number of cars at 11 am.

The number of cars at 10 am is decreasing faster than the number of cars at 8 pm.

The number of cars 9:00 am is increasing slower than the number of cars at 8:30 am.

The number of cars at 3 pm is increasing slower than the number of cars 6:30 pm.

Let's analyze the graph and evaluate the statements systematically.

### Graph Overview:
- **X-axis**: Hours after midnight (from 0 to 22 hours).
- **Y-axis**: Number of cars in hundreds (from 0 to 9).
- The graph shows two peaks: 
  - Around **9 am** (peak around 4.5 hundred cars).
  - Around **7-8 pm** (peak near 9 hundred cars).
- There are dips after both peaks (from around **10 am** and **8 pm** respectively).

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### Evaluating the Statements:
1. **"The number of cars at 10 am is decreasing faster than the number of cars at 11 am."**
   - **10 am** lies on the steep downward slope following the first peak at 9 am.
   - **11 am** shows a shallower decline as the curve flattens.
   - **True**: The slope is steeper at 10 am, meaning the rate of decrease is faster than at 11 am.

2. **"The number of cars at 10 am is decreasing faster than the number of cars at 8 pm."**
   - At **10 am**, the curve shows a steep decline, while at **8 pm**, it has reached the second peak, and the number of cars starts to drop only slightly afterward.
   - **True**: The decline at 10 am is faster than at 8 pm.

3. **"The number of cars at 9:00 am is increasing slower than the number of cars at 8:30 am."**
   - Around **8:30 am**, the graph is rising rapidly (the slope is steep).
   - At **9 am**, the graph reaches its first peak, meaning the increase is slowing down.
   - **True**: The increase is slower at 9:00 am compared to 8:30 am.

4. **"The number of cars at 3 pm is increasing slower than the number of cars at 6:30 pm."**
   - At **3 pm**, the curve is relatively flat, indicating only a small increase.
   - Around **6:30 pm**, the graph is rising sharply towards the evening peak.
   - **True**: The increase at 3 pm is slower than the increase at 6:30 pm.

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### Conclusion:
All four statements are **true** based on the shape of the graph and the slopes at the respective times.

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Do you need further clarification or details?

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Here are five follow-up questions related to this graph:
1. What is the peak number of cars in the lot during the day, and at what time does it occur?
2. How many cars are in the lot at noon (12 pm)?
3. How can we calculate the rate of change of cars in the lot between 7 am and 9 am?
4. What time interval shows the steepest decrease in the number of cars?
5. Can you find two time intervals with roughly equal slopes (either increasing or decreasing)?

**Tip:** When comparing slopes on a graph, the steeper the slope, the faster the rate of increase or decrease.

The graph shows the number of cars in the parking lot of a major retailer (in hundreds) in the hours after midnight. What is true about this graph? The number of cars at 10 am is decreasing faster than the number of cars at 11 am. The number of cars at 10 am is decreasing faster than the number of cars at 8 pm. The number of cars 9:00 am is increasing slower than the number of cars at 8:30 am. The number of cars at 3 pm is increasing slower than the number of cars 6:30 pm.

Analyze the number of cars in a parking lot over the hours after midnight. This problem involves interpreting a graph to compare slopes and the rate of change. Learn how to determine the faster or slower decrease or increase at different times of the day. Suitable for students in Grades 9-12.

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