Question

Use the image to answer the question. Analyze the tile pattern and write a function for the pattern. Use x for the image number and y for the number of tiles in each image
The function modeled by the pattern is --, since the slope is--- and the y-intercept is ---.

Answer 1

To analyze a tile pattern and write a function for it, we'll need to determine how the number of tiles (y) corresponds to the image number (x). Since I cannot view images, let's break down how you would typically approach this problem.

1. **Identify the Pattern:**
- Observe how the number of tiles increases as you go from one image number to the next. Is it a linear pattern, quadratic, or exponential?

2. **Determine the Slope:**
- For a linear relationship, the slope (m) can be calculated as:
\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]
- Take two points from the pattern (for example, (x1, y1) and (x2, y2)) to calculate this.

3. **Find the y-intercept:**
- The y-intercept (b) is the value of y when x = 0. If your pattern starts at a specific number of tiles, this is often the value of y when you plug in x = 0.

4. **Write the function:**
- The equation of the line based on slope-intercept form is:
\[
y = mx + b
\]

### Example Scenario:
Imagine you determined that the number of tiles is increasing by 3 tiles for each image number:

- For image 0 (x=0), y=2 (2 tiles)
- For image 1 (x=1), y=5 (5 tiles)
- For image 2 (x=2), y=8 (8 tiles)

In this scenario,
- The slope (m) is 3 (since 5 - 2 = 3 for x moving from 0 to 1 and 8 - 5 = 3 for x moving from 1 to 2).
- The y-intercept (b) is 2.

### Final Function:
Thus, your function would be:
\[
y = 3x + 2
\]
- The function modeled by the pattern is **y = 3x + 2**, since the slope is **3** and the y-intercept is **2**.

Replace the example values with the actual ones you derive from your pattern to finalize your function.