https://file.aiquickdraw.com/mathbot/file/1727413460146k81d9sfr.jpg

The task asks for creating a table and a graph to match the given tile pattern, then fully describing the graph.

### Step 1: Identify the tile pattern.
- **Figure 2** has 6 tiles.
- **Figure 3** has 9 tiles.
- **Figure 4** has 12 tiles.

We can assume the pattern continues linearly, as the number of tiles increases by 3 with each figure. This suggests a consistent growth rate.

### Step 2: Create a table.

| Figure Number (x) | Number of Tiles (y) |
|-------------------|---------------------|
| 2                 | 6                   |
| 3                 | 9                   |
| 4                 | 12                  |

The pattern shows that the number of tiles increases by 3 for each new figure.

### Step 3: Find the relationship between figure number and number of tiles.
The relationship is linear, and we can express it as:

\[
y = 3x
\]

Where:
- \( y \) is the number of tiles,
- \( x \) is the figure number.

For example:
- When \( x = 2 \), \( y = 3(2) = 6 \),
- When \( x = 3 \), \( y = 3(3) = 9 \),
- When \( x = 4 \), \( y = 3(4) = 12 \).

### Step 4: Plot the graph.
The points to plot are:
- (2, 6)
- (3, 9)
- (4, 12)

The graph is a straight line with a slope of 3, showing that for each increase in the figure number by 1, the number of tiles increases by 3.

### Step 5: Describe the graph.
- The graph is a straight line with a positive slope of 3.
- The line starts at (2, 6) and passes through (3, 9) and (4, 12), following the linear equation \( y = 3x \).
- The slope indicates that the number of tiles increases by 3 for each additional figure number.
- The graph is defined only for integer values of \( x \) (Figure numbers), as fractional figures don't make sense in this context.

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Would you like more details on this solution or any specific part? Here are some related questions:

1. How would the equation change if the growth in tiles was different?
2. Can you explain how to calculate the slope of the line?
3. What if Figure 1 had tiles? How would it affect the equation?
4. How do you extend the table for Figure 5 and beyond?
5. What is the importance of using a linear function in this context?

**Tip**: When analyzing patterns, identifying the growth rate (e.g., how much the number of tiles increases) is crucial for forming the equation!

Create a table and graph to match the tile pattern in the provided figures. Then fully describe the graph.

Learn how to recognize tile patterns and graph them with a linear equation. This problem involves plotting points for tile figures, finding a pattern, and describing the graph. Suitable for middle school students.

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