1. **State the problem:** Solve the linear equation $4x - y = 6$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving other terms to the opposite side. 3. **Isolate $y$:** $$4x - y = 6$$ Subtract $4x$ from both sides: $$\cancel{4x} - y - \cancel{4x} = 6 - 4x$$ which simplifies to $$-y = 6 - 4x$$ 4. **Solve for $y$:** Multiply both sides by $-1$ to get $y$ positive: $$-1 \times (-y) = -1 \times (6 - 4x)$$ which gives $$y = -6 + 4x$$ 5. **Final answer:** $$y = 4x - 6$$ This expresses $y$ as a function of $x$.