To find the number of centimeters in 1 inch based on the relationship \( 6y = 15.24x \), we can first rewrite the equation in a more straightforward way.
Here, \( y \) represents the number of centimeters, and \( x \) represents the number of inches. The current relationship tells us that for 6 inches (when \( x = 6 \)), we have 15.24 centimeters (when \( y = 15.24 \)).
To determine the number of centimeters in 1 inch, we could set up the ratio:
\[ \frac{y}{x} = \frac{15.24}{6} \]
Now, calculate the value:
\[ \frac{15.24}{6} = 2.54 \]
This tells us that for every inch (1 inch), there are 2.54 centimeters.
Thus, the correct answer is:
2.54 centimeters.