To analyze the pattern and find the function relating the image number (x) to the number of tiles (y), we first need to gather the information from the configurations (images 1 to 4) you mentioned. Although I can't see the images, I can guide you on how to derive a linear equation based on the slope and y-intercept.
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Identify Points: For each image number (x), identify the corresponding number of tiles (y).
- For example, if:
- Image 1 has 3 tiles (1, 3)
- Image 2 has 5 tiles (2, 5)
- Image 3 has 7 tiles (3, 7)
- Image 4 has 9 tiles (4, 9)
- For example, if:
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Determine Slope (m): The slope (m) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] From the example:
- Between images 1 and 2: \[ m = \frac{5 - 3}{2 - 1} = \frac{2}{1} = 2 \] Thus, the slope is 2.
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Find Y-intercept (b): To find the y-intercept, you can set x = 0 and solve for y. Alternatively, you can use any point (x, y) in the equation \(y = mx + b\) and rearrange to find b.
- Using point (1, 3): \[ 3 = 2(1) + b \implies 3 = 2 + b \implies b = 1 \] So, the y-intercept is 1.
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Compose the Function: With the slope (m) and y-intercept (b), write the linear equation: \[ y = 2x + 1 \]
In conclusion, fill in the final responses:
- The function modeled by the pattern is \( y = 2x + 1 \), since the slope is \( 2 \) and the y-intercept is \( 1 \).
Replace the example values with your actual observations for accurate results.