1. **State the problem:** Find the inverse function of $f(x) = -\frac{4}{5}x + 8$ in slope-intercept form $y = mx + b$. 2. **Recall the formula and rules:** To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in the equation and then solve for $y$. 3. **Start with the original function:** $$y = -\frac{4}{5}x + 8$$ 4. **Swap $x$ and $y$:** $$x = -\frac{4}{5}y + 8$$ 5. **Solve for $y$:** Subtract 8 from both sides: $$x - 8 = -\frac{4}{5}y$$ 6. **Isolate $y$ by dividing both sides by $-\frac{4}{5}$:** $$y = \frac{x - 8}{-\frac{4}{5}}$$ 7. **Simplify the division by a fraction:** $$y = (x - 8) \times \frac{5}{-4} = (x - 8) \times -\frac{5}{4}$$ 8. **Distribute the multiplication:** $$y = -\frac{5}{4}x + \frac{5}{4} \times 8$$ 9. **Calculate the constant term:** $$\frac{5}{4} \times 8 = \frac{5}{4} \times \frac{8}{1} = \frac{40}{4} = 10$$ 10. **Write the inverse function:** $$f^{-1}(x) = -\frac{5}{4}x + 10$$ **Final answer:** $$\boxed{f^{-1}(x) = -\frac{5}{4}x + 10}$$