1. **State the problem:** Solve the equation $\frac{y}{x} = 2$ for $y$ in terms of $x$. 2. **Formula and rules:** The equation shows a ratio of $y$ to $x$ equal to 2. To isolate $y$, multiply both sides by $x$ (assuming $x \neq 0$). 3. **Intermediate work:** $$\frac{y}{x} = 2$$ Multiply both sides by $x$: $$\cancel{x} \cdot \frac{y}{\cancel{x}} = 2 \cdot x$$ This simplifies to: $$y = 2x$$ 4. **Explanation:** Multiplying both sides by $x$ cancels the denominator on the left side, leaving $y$ alone. The right side becomes $2x$, so $y$ is twice $x$. 5. **Final answer:** $$y = 2x$$