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The given table shows the number of tiles (\(t\)) and the corresponding perimeter (\(P\)) of a figure made from square tiles. 

| Number of Tiles (\(t\)) | Perimeter (\(P\)) |
|-------------------------|-------------------|
| 1                       | 8                 |
| 2                       | 12                |
| 3                       | 16                |

We are asked to find the equation that best models this pattern.

### Step 1: Identify the pattern
From the table, we can observe the following:
- For \( t = 1 \), \( P = 8 \)
- For \( t = 2 \), \( P = 12 \)
- For \( t = 3 \), \( P = 16 \)

It seems that the perimeter increases by 4 units for every additional tile. This suggests a linear relationship between \( t \) and \( P \), where the slope of the line is 4.

### Step 2: Formulate the equation
We know the slope of the line is 4, meaning the equation is of the form:
\[ P = 4t + b \]
To find \( b \), substitute one of the points from the table. Let's use \( t = 1 \) and \( P = 8 \):
\[
8 = 4(1) + b \\
b = 8 - 4 = 4
\]
Thus, the equation that models the pattern is:
\[
P = 4t + 4
\]

### Step 3: Compare with the given choices
- A. \( P = t + 7 \) – Incorrect
- B. \( P = 4t + 4 \) – Correct
- C. \( P = 4t \) – Incorrect, missing the constant
- D. \( P = 8t \) – Incorrect, wrong slope

The correct answer is **B. \( P = 4t + 4 \)**.

Would you like a detailed breakdown of any of the steps or concepts?

### Related Questions:
1. How do you calculate the slope of a line from a table of values?
2. What is the significance of the constant in a linear equation?
3. How can you verify if a relationship is linear from a table?
4. What would the perimeter be if the number of tiles was \( t = 5 \)?
5. How would the equation change if each tile added 5 units to the perimeter?

**Tip**: To identify a linear pattern, check how the dependent variable changes as the independent variable increases by a constant amount.

Which equation best models the relationship between the number of tiles and the perimeter of a figure made from square tiles?

Explore how to model the perimeter of a figure made from square tiles with a linear equation. Learn how to recognize patterns in a table and derive the equation P = 4t + 4. Suitable for Grades 7-9 students looking to strengthen their understanding of linear relationships.

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