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Let's break down the information in the problem step by step to construct a graph of Landon's distance from home over time.

### Step-by-Step Solution

1. **First Segment (0 - 6 blocks, 0 - 2 minutes):**
   - **Starting Point:** Time \( t = 0 \), blocks from home = \( 0 \).
   - He drives 6 blocks to the store at a speed of 3 blocks per minute.
   - Time to reach the store \( = \frac{6 \text{ blocks}}{3 \text{ blocks/min}} = 2 \) minutes.
   - **End of Segment:** At \( t = 2 \) minutes, he is 6 blocks from home.

2. **Second Segment (7-minute stop at the store):**
   - Landon stops at the store for 7 minutes.
   - **Time Interval:** \( t = 2 \) to \( t = 9 \) minutes (2 minutes + 7 minutes).
   - Distance from home remains at 6 blocks during this interval.

3. **Third Segment (6 - 10 blocks, 9 - 11 minutes):**
   - He then drives 4 additional blocks to the bank at a speed of 2 blocks per minute.
   - Time to reach the bank \( = \frac{4 \text{ blocks}}{2 \text{ blocks/min}} = 2 \) minutes.
   - **Time Interval:** \( t = 9 \) to \( t = 11 \) minutes.
   - **End of Segment:** At \( t = 11 \) minutes, he is 10 blocks from home.

4. **Fourth Segment (5-minute stop at the bank):**
   - Landon stops at the bank for 5 minutes.
   - **Time Interval:** \( t = 11 \) to \( t = 16 \) minutes.
   - Distance from home remains at 10 blocks during this interval.

5. **Fifth Segment (Return to home, 10 - 0 blocks, 16 - 18 minutes):**
   - He drives back home from the bank at a speed of 5 blocks per minute.
   - Distance to home = 10 blocks.
   - Time to get home \( = \frac{10 \text{ blocks}}{5 \text{ blocks/min}} = 2 \) minutes.
   - **End of Segment:** At \( t = 18 \) minutes, he is back at home, 0 blocks away.

### Summary Table of Distances at Key Times

| Time (minutes) | Distance from Home (blocks) | Event                        |
|----------------|-----------------------------|------------------------------|
| 0              | 0                           | Starts driving               |
| 2              | 6                           | Arrives at store             |
| 9              | 6                           | Finishes stop at store       |
| 11             | 10                          | Arrives at bank              |
| 16             | 10                          | Finishes stop at bank        |
| 18             | 0                           | Arrives back home            |

### Graph Interpretation

In the graph of this function:
- The **x-axis** will represent time in minutes.
- The **y-axis** will represent distance from home in blocks.
- The graph will have segments where it rises (when he is driving away), stays flat (when he is stopped), and falls (when he is returning home).

Would you like me to plot this graph for you, or do you have questions about any of these steps?

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### Related Questions

1. What would happen to the graph if Landon traveled at a slower speed on his return trip?
2. How would the graph change if Landon made an additional stop on his way home?
3. Can we write a piecewise function to represent Landon’s distance from home over time?
4. What would be the impact on the graph if he stopped for longer at the bank?
5. How does changing the speed affect the time intervals on the graph?

### Tip

When interpreting distance-time graphs, a horizontal line represents a stationary period, while a slope (positive or negative) indicates movement at a specific rate.

Landon left his house at time zero and drove to the store, which is 6 blocks away, at a speed of 3 blocks per minute. Then he stopped and went into the store for 7 minutes. From there, he drove in the same direction at a speed of 2 blocks per minute until he got to the bank, which is 4 blocks away from the store. He stopped at the bank for 5 minutes. Then he drove home at a speed of 5 blocks every minute. Make a graph of showing the number of blocks away from home that Landon is x minutes after he leaves his house, until he gets back home.

Learn how to create a distance-time graph based on Landon’s trip to the store and bank, incorporating speed, stops, and changes in direction. This problem covers key concepts in linear equations and piecewise functions, ideal for students in Grades 8-10.

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