1. **State the problem:** Solve the linear equation $x - y = 8$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by performing algebraic operations. 3. **Isolate $y$:** Starting with the equation: $$x - y = 8$$ Subtract $x$ from both sides: $$x - y - x = 8 - x$$ which simplifies to: $$-y = 8 - x$$ 4. **Cancel the negative sign:** Multiply both sides by $-1$ to solve for $y$: $$\cancel{-}y \times \cancel{-}1 = (8 - x) \times -1$$ which gives: $$y = -8 + x$$ 5. **Rewrite the solution:** The equation solved for $y$ is: $$y = x - 8$$ 6. **Interpretation:** This means for any value of $x$, $y$ is $8$ less than $x$. The graph is a straight line with slope $1$ and $y$-intercept $-8$. **Final answer:** $$y = x - 8$$