1. **State the problem:** Solve the linear equation $3x - 4y = 18$ 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 $y$:** $$3x - 4y = 18$$ Subtract $3x$ from both sides: $$\cancel{3x} - 4y - \cancel{3x} = 18 - 3x$$ which simplifies to $$-4y = 18 - 3x$$ 4. **Divide both sides by $-4$ to solve for $y$:** $$y = \frac{18 - 3x}{-4} = \frac{\cancel{18} - 3x}{\cancel{-4}}$$ Show cancellation explicitly: $$y = \frac{18 - 3x}{-4} = \frac{18}{-4} - \frac{3x}{-4} = -\frac{18}{4} + \frac{3x}{4}$$ 5. **Simplify fractions:** $$y = -\frac{9}{2} + \frac{3}{4}x$$ 6. **Final answer:** $$y = \frac{3}{4}x - \frac{9}{2}$$ This expresses $y$ in terms of $x$ for the given linear equation.