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.
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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?
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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.
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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.
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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.
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