To create a function that describes the relationship between the image number \( x \) and the number of tiles \( y \) based on the configurations labeled 1–4, we would typically identify the pattern in tile counts for each image number.
Assuming we have the tile counts as follows (note that these are just hypothetical examples since I do not have access to the actual image):
- Image 1: 2 tiles
- Image 2: 4 tiles
- Image 3: 6 tiles
- Image 4: 8 tiles
Based on these hypothetical counts, we can see that as the image number increases by 1, the number of tiles increases by 2. This suggests a linear relationship.
The function that describes this pattern in slope-intercept form \( y = mx + b \) can be formulated as:
- \( m \) (slope) = change in \( y \) / change in \( x \) = (4 - 2) / (2 - 1) = 2
- \( b \) (y-intercept) = the value of \( y \) when \( x = 0 \). If no constant term is needed in real examples, assume \( b = 0 \).
So the function would be: \[ y = 2x \]
Thus, we can summarize:
- The function modeled by the pattern is \( y = 2x \), since the slope is \( 2 \) and the y-intercept is \( 0 \).
Make sure to substitute the actual tile numbers you observe for a precise function.
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