1. **State the problem:** Solve the linear equation $5x + 2y = 17$ 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 and then dividing by the coefficient of $y$. 3. **Isolate $y$:** $$5x + 2y = 17$$ Subtract $5x$ from both sides: $$\cancel{5x} + 2y - \cancel{5x} = 17 - 5x$$ which simplifies to $$2y = 17 - 5x$$ 4. **Divide both sides by 2 to solve for $y$:** $$y = \frac{17 - 5x}{2}$$ Show the cancellation explicitly: $$y = \frac{\cancel{2} \cdot \frac{17 - 5x}{\cancel{2}}}{1} = \frac{17 - 5x}{2}$$ 5. **Final answer:** $$y = \frac{17 - 5x}{2}$$ This expresses $y$ in terms of $x$ for the given linear equation.