Draw Graph from Story - Free Printable

Problem Analysis:

We need to create a graph showing the number of blocks Isaiah is away from his house as a function of time, \( x \) minutes after he leaves his house. The problem involves three distinct phases:

1. Driving to the store: Isaiah drives at a speed of 3 blocks every 2 minutes for 6 minutes.
2. Stopping at the store: Isaiah stops and stays in the store for 2 minutes.
3. Driving back home: Isaiah drives back at a speed of 3 blocks every 4 minutes.

Step-by-Step Solution:

#### Phase 1: Driving to the store
- Speed: 3 blocks every 2 minutes.
- Time: 6 minutes.
- Distance Calculation:
\[
\text{Distance} = \left( \frac{3 \text{ blocks}}{2 \text{ minutes}} \right) \times 6 \text{ minutes} = 9 \text{ blocks}
\]
- Graph Behavior: The distance increases linearly from 0 blocks at \( t = 0 \) to 9 blocks at \( t = 6 \).

#### Phase 2: Stopping at the store
- Duration: 2 minutes.
- Distance: Isaiah remains 9 blocks away from home during this time.
- Graph Behavior: The distance remains constant at 9 blocks from \( t = 6 \) to \( t = 8 \).

#### Phase 3: Driving back home
- Speed: 3 blocks every 4 minutes.
- Initial Distance: 9 blocks.
- Final Distance: 0 blocks (back home).
- Time Calculation:
\[
\text{Time to travel 9 blocks} = \left( \frac{4 \text{ minutes}}{3 \text{ blocks}} \right) \times 9 \text{ blocks} = 12 \text{ minutes}
\]
- However, since Isaiah starts driving back at \( t = 8 \), the total time to return home is from \( t = 8 \) to \( t = 20 \).
- Graph Behavior: The distance decreases linearly from 9 blocks at \( t = 8 \) to 0 blocks at \( t = 20 \).

Graph Construction:

We will plot the distance from home (\( y \)-axis) against time (\( x \)-axis).

1. From \( t = 0 \) to \( t = 6 \):
- Distance increases linearly from 0 to 9 blocks.
- Slope: \( \frac{9 \text{ blocks}}{6 \text{ minutes}} = 1.5 \text{ blocks per minute} \).

2. From \( t = 6 \) to \( t = 8 \):
- Distance remains constant at 9 blocks.

3. From \( t = 8 \) to \( t = 20 \):
- Distance decreases linearly from 9 blocks to 0 blocks.
- Slope: \( \frac{0 - 9 \text{ blocks}}{20 - 8 \text{ minutes}} = \frac{-9}{12} = -0.75 \text{ blocks per minute} \).

Plotting the Graph:

- Points to Plot:
- At \( t = 0 \): \( (0, 0) \)
- At \( t = 6 \): \( (6, 9) \)
- At \( t = 8 \): \( (8, 9) \)
- At \( t = 20 \): \( (20, 0) \)

- Connecting the Points:
- Draw a straight line from \( (0, 0) \) to \( (6, 9) \).
- Draw a horizontal line from \( (6, 9) \) to \( (8, 9) \).
- Draw a straight line from \( (8, 9) \) to \( (20, 0) \).

Final Answer:

The graph should show:
- A rising line from \( (0, 0) \) to \( (6, 9) \).
- A horizontal line from \( (6, 9) \) to \( (8, 9) \).
- A falling line from \( (8, 9) \) to \( (20, 0) \).

\[
\boxed{\text{Graph as described above}}
\]