1. **State the problem:** Solve the linear equation $8x - 2y = 5$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we use basic algebraic operations: addition, subtraction, multiplication, and division. 3. **Isolate $y$:** $$8x - 2y = 5$$ Subtract $8x$ from both sides: $$-2y = 5 - 8x$$ 4. **Divide both sides by $-2$ to solve for $y$:** $$y = \frac{5 - 8x}{-2}$$ Show cancellation of the negative sign: $$y = \frac{\cancel{5 - 8x}}{\cancel{-2}} = -\frac{5}{2} + 4x$$ 5. **Final answer:** $$y = 4x - \frac{5}{2}$$ This means for any value of $x$, you can find $y$ using this formula.