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 $x$. To isolate $y$, multiply both sides by $x$. 3. **Intermediate work:** $$\frac{y}{x} = 2$$ Multiply both sides by $x$: $$\cancel{x} \times \frac{y}{\cancel{x}} = 2 \times x$$ 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 $x$. **Final answer:** $$y = 2x$$