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.

(2 points)
The function modeled by the pattern is
, since the slope is
and the y-intercept is
.

Answer 1

To analyze the tile pattern and create a function, we need more specific information about how the number of tiles (y) relates to the image number (x). Since I don't have a visual representation of the tile pattern or explicit data points related to the pattern, let's create a general approach for determining the relationship.

### Step-by-step Analysis:

1. **Identify the Pattern**:
- Look for the relationship between image number (x) and the number of tiles (y).
- For example, if the first image has 2 tiles, the second has 4 tiles, and the third has 6 tiles, we would observe a linear increase.

2. **Determine the Slope (m)**:
- The slope can be found by calculating the change in the number of tiles per change in the image number. For instance, if each additional image adds 2 tiles:
\[
m = \frac{\Delta y}{\Delta x} = \frac{2}{1} = 2
\]

3. **Determine the y-intercept (b)**:
- The y-intercept is the value of y when x = 0. If there are no tiles at the starting point (x = 0), then b = 0, or if the first image number leads to a non-zero count, that value would be b.

### Example Function:

Assuming the pattern is that for each image added, there are 2 additional tiles, and starting from a base of 0 tiles when there are no images, we can write a function:

- **Function**:
\[
y = 2x
\]

- **Slope (m)**:
- Slope is 2 (indicating the number of tiles increases by 2 for each additional image).

- **Y-intercept (b)**:
- Y-intercept is 0 (indicating there are 0 tiles when x = 0).

### Conclusion:
Putting it together, you can express the modeled function by stating:

The function modeled by the pattern is \( y = 2x \), since the slope is 2 and the y-intercept is 0.

If you provide specific numbers from the tile patterns, I can refine this function to fit that specific dataset.