The equation you provided is:

$\frac{10}{y} = \frac{2}{9}$

To solve for $y$, follow these steps:

Step 1: Cross-multiply

You can cross-multiply to eliminate the fractions:

$10 \times 9 = 2 \times y$

This simplifies to:

$90 = 2y$

Step 2: Solve for $y$

Now, divide both sides of the equation by 2 to isolate $y$:

$y = \frac{90}{2} = 45$

Final Answer:

$y = 45$

Would you like a further explanation or to verify this result? Here are some additional related questions:

1. How would you solve for $y$ if the equation was $\frac{10}{y} = \frac{3}{8}$?
2. What happens if the equation had a negative fraction (e.g., $\frac{10}{y} = \frac{-2}{9}$)?
3. How do you check if your solution is correct by substituting $y = 45$ back into the equation?
4. How can this technique be applied to more complex fractional equations?
5. Can you set up and solve a similar proportion where $y$ is in the numerator, e.g., $\frac{y}{10} = \frac{2}{5}$?

Tip: Cross-multiplying is a powerful tool for solving equations with fractions. Just be careful to keep terms balanced on both sides.