To solve the proportion \( \frac{15}{2} = \frac{75}{y} \), we can use cross-multiplication. This means we will multiply the numerator of one fraction by the denominator of the other fraction and set the two products equal to each other.
Cross-multiplying gives us:
\[ 15y = 2 \cdot 75 \]
Now compute \( 2 \cdot 75 \):
\[ 2 \cdot 75 = 150 \]
Now we have the equation:
\[ 15y = 150 \]
Next, we will solve for \( y \) by dividing both sides by 15:
\[ y = \frac{150}{15} \]
Calculating \( \frac{150}{15} \):
\[ y = 10 \]
Thus, the solution is:
\[ y = 10 \]