1. **State the problem:** We need to translate the statement "a varies inversely with b" into an equation. 2. **Recall the formula for inverse variation:** If a quantity $a$ varies inversely with $b$, it means that as $b$ increases, $a$ decreases such that their product is constant. The formula is: $$a \times b = k$$ where $k$ is the constant of variation. 3. **Write the equation:** From the statement, the equation representing the relationship is: $$a = \frac{k}{b}$$ 4. **Explain:** This means $a$ is equal to some constant $k$ divided by $b$. As $b$ gets larger, $a$ gets smaller, and vice versa, maintaining the product $ab = k$. **Final answer:** $$a = \frac{k}{b}$$