To find the inverse of the given function $y = 3x + 8$, we need to follow these steps:

1. Replace $y$ with $x$ (swap $x$ and $y$) to represent the inverse function: $x = 3y + 8$

2. Solve for $y$ in terms of $x$: $x - 8 = 3y$ $y = \frac{x - 8}{3}$

3. Rewrite the result in the form $y = ax + b$: $y = \frac{1}{3}x - \frac{8}{3}$

Thus, the inverse function is: $y = \frac{1}{3}x - \frac{8}{3}$

Let me know if you have questions or need further details!

Here are some follow-up questions to expand on this topic:

1. How do you verify that two functions are inverses of each other?
2. What is the graphical interpretation of the inverse of a function?
3. What happens to the domain and range of the original function when finding the inverse?
4. Can you determine the inverse of a quadratic function? How is the process different?
5. How would you rewrite $y = \frac{1}{3}x - \frac{8}{3}$ in terms of slope-intercept form?

Tip: Remember that the inverse of a linear function always reflects across the line $y = x$.