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
.

1 answer

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.