To find the number of centimeters in 1 inch using the proportional relationship given in the equation \(6y = 15.24x\), we can analyze the equation and isolate \(y\).
Given that:
\[ 6y = 15.24x \]
To solve for \(y\), we divide both sides by 6:
\[ y = \frac{15.24}{6}x \]
To find the value of \(y\) when \(x = 1\) (which represents 1 inch), we have:
\[ y = \frac{15.24}{6} \cdot 1 \]
Calculating \(y\):
\[ y = \frac{15.24}{6} \approx 2.54 \]
Thus, \(y \approx 2.54\), which means that there are approximately 2.54 centimeters in 1 inch.
Therefore, the correct response is:
2.54 centimeters.
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