1. **State the problem:** Solve the linear equation $3x - y = 7$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving all other terms to the opposite side. 3. **Isolate $y$:** Starting with the equation: $$3x - y = 7$$ Subtract $3x$ from both sides: $$3x - y - 3x = 7 - 3x$$ Which simplifies to: $$-y = 7 - 3x$$ 4. **Divide both sides by $-1$ to solve for $y$:** $$\cancel{-}y = 7 - 3x$$ $$\frac{\cancel{-}y}{\cancel{-}} = \frac{7 - 3x}{-1}$$ 5. **Simplify the right side:** $$y = -7 + 3x$$ 6. **Final answer:** $$y = 3x - 7$$ This means for any value of $x$, you can find $y$ by multiplying $x$ by 3 and then subtracting 7.