To find the number of centimeters in 1 inch based on the proportional relationship given by the equation \(6y = 15.24x\), we can start by isolating \(y\).
The equation can be rewritten as:
\[ y = \frac{15.24}{6}x \]
Now, we can divide \(15.24\) by \(6\):
\[ y \approx 2.54x \]
This means that \(y\) (the number of centimeters) is approximately \(2.54\) times \(x\) (the number of inches). Therefore, there are approximately \(2.54\) centimeters in \(1\) inch.
So the correct response is:
2.54 centimeters.