1. **State the problem:** Find the inverse of the function $y = -3x + 4$. 2. **Recall the formula and rule:** To find the inverse of a function, swap $x$ and $y$ and then solve for $y$. 3. **Swap variables:** Replace $y$ with $x$ and $x$ with $y$: $$x = -3y + 4$$ 4. **Solve for $y$:** $$x - 4 = -3y$$ 5. **Isolate $y$:** $$\frac{x - 4}{-3} = y$$ 6. **Simplify the fraction:** $$y = -\frac{x - 4}{3} = -\frac{x}{3} + \frac{4}{3}$$ 7. **Write the inverse function:** $$y^{-1} = -\frac{1}{3}x + \frac{4}{3}$$ **Answer:** The inverse function is $$y^{-1} = -\frac{1}{3}x + \frac{4}{3}$$.