To determine the equation that represents the relationship between the side length \(x\) and the perimeter \(y\) of squares, we can recall that the perimeter \(y\) of a square is calculated using the formula:
\[ y = 4x \]
where \(x\) is the side length.
Let's check the provided data with this formula to validate that this relationship holds:
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For \(x = 4.5\): \[ y = 4 \times 4.5 = 18 \]
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For \(x = 8.5\): \[ y = 4 \times 8.5 = 34 \]
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For \(x = 10.25\): \[ y = 4 \times 10.25 = 41 \]
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For \(x = 13.75\): \[ y = 4 \times 13.75 = 55 \]
Since all the calculated values for \(y\) match the given perimeters, the correct equation that represents the relationship between the side length \(x\) and the perimeter \(y\) is:
\[ y = 4x \]