1. **State the problem:** Solve the linear equation $5x - 4y = 1$ for $y$ in terms of $x$. 2. **Formula and rules:** To express $y$ as a function of $x$, isolate $y$ on one side of the equation. 3. **Isolate $y$:** $$5x - 4y = 1$$ Subtract $5x$ from both sides: $$-4y = 1 - 5x$$ 4. **Divide both sides by $-4$ to solve for $y$:** $$y = \frac{1 - 5x}{-4}$$ Show cancellation: $$y = \frac{\cancel{1} - 5x}{\cancel{-4}} = -\frac{1}{4} + \frac{5}{4}x$$ 5. **Rewrite in slope-intercept form:** $$y = \frac{5}{4}x - \frac{1}{4}$$ **Final answer:** $$y = \frac{5}{4}x - \frac{1}{4}$$ This is the equation of the line in slope-intercept form, where the slope is $\frac{5}{4}$ and the y-intercept is $-\frac{1}{4}$.