Use the image to answer the question.

Question

Four different configurations of tiles are labeled 1–4.

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 create a function that represents the pattern of tiles based on the configuration images labeled 1–4, we first need to identify the relationship between the image number (x) and the number of tiles (y).

Assuming you have observed the tile configurations for images 1 to 4, the pattern can be derived from the counts as follows:

1. Identify the values for x and y:

   • Image 1 (x = 1): y = number of tiles
   • Image 2 (x = 2): y = number of tiles
   • Image 3 (x = 3): y = number of tiles
   • Image 4 (x = 4): y = number of tiles

2. Determine the slope (m):

   • The slope indicates how many additional tiles are added for each subsequent configuration. It is determined by the change in the number of tiles (Δy) divided by the change in the image number (Δx).

3. Determine the y-intercept (b):

   • The y-intercept indicates the starting point of the function when x = 0. It can often be inferred if the pattern follows a linear growth starting from a base amount (which might be zero or a nonzero number based on the configurations).

Given these considerations, you can write the function in the form:

\[ y = mx + b \]

Where:

• \( m \) is the slope (the number of additional tiles added for each increment in x),
• \( b \) is the y-intercept (the number of tiles when x = 0).

Example Conclusion

The function modeled by the pattern is \( y = mx + b \), since the slope is \( m \) (the calculated increment of tiles per image) and the y-intercept is \( b \) (the starting count of tiles when x = 0).

To fill in the specific values for \( m \) and \( b \), you would need to provide the actual counts of tiles for each image configuration from the referred image.

Answer 2

The function modeled by the pattern is _, since the slope is _ and the y-intercept is 0

Answer 3

To fill in the blanks for your statement using a linear model for tile patterns, you could express the function as follows:

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

In this context:

• \( y \) represents the number of tiles.
• \( x \) represents the image number.
• \( m \) can be calculated based on the patterns observed in the tile configurations.

Example Utilization:

If you identified that for each subsequent image (from 1 to 4), the number of tiles increased by a consistent amount, you can replace \( m \) with that specific value. For example, if the number of tiles increased by 2 for each image:

• The function would be \( y = 2x \), with a slope of 2 and a y-intercept of 0.

Feel free to replace \( m \) with the actual value based on your analysis of the tiles, assuming the y-intercept remains 0 as mentioned.

Answer 4

2x and 2 are wrong

Answer 5

I apologize for the confusion. To accurately provide the function, I need to understand the specific pattern of tile counts in the images. Since I can't see the image, I'll offer a general template for completing your statement given the correct slope (m) based on your observation.

To finalize your statement:

The function modeled by the pattern is \( y = mx \), since the slope is (actual value of m you have observed) and the y-intercept is 0.

Steps to Find the Correct Values:

1. Identify Tile Counts: Count the number of tiles in each image (1 to 4).
2. Calculate the Slope (m): Determine how many additional tiles there are from one image to the next.
   • For example, if Image 1 has 3 tiles, Image 2 has 5 tiles, Image 3 has 7 tiles, and Image 4 has 9 tiles, the slope would be 2.
3. Confirm Y-Intercept: Since you stated the y-intercept is 0, this indicates that the function starts at the origin (0,0).

Let's say, for instance, the counts of tiles are:

• Image 1: 1 tile
• Image 2: 3 tiles
• Image 3: 5 tiles
• Image 4: 7 tiles

In this case:

• The slope \( m \) is 2 (since it increases by 2 for each image),
• The y-intercept \( b \) is 0 (since at \( x = 0 \), \( y = 0 \)).

Thus, the complete statement would be:

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

Please replace the values of \( m \) with the values that match the configuration you’ve analyzed. If you provide the actual number of tiles for each image, I can help find the specific slope!