To find the inverse of the equation $y = \frac{3}{2}x$, follow these steps:

1. Replace $y$ with $x$ and $x$ with $y$: $x = \frac{3}{2}y$

2. Solve for $y$: $y = \frac{2}{3}x$

Therefore, the inverse of the equation $y = \frac{3}{2}x$ is:

C. $y = \frac{2}{3}x$

Would you like further details or have any questions?

Here are 8 related questions to expand your understanding:

1. What is the general method to find the inverse of any linear function?
2. How do you determine if a given function is one-to-one?
3. Can the inverse of a function be found if the function is not one-to-one? Explain.
4. How do you graph the inverse of a linear function?
5. What is the geometric interpretation of the inverse on the coordinate plane?
6. How does finding the inverse of a linear function differ from finding the inverse of a non-linear function?
7. What is the significance of the slope in the context of a function and its inverse?
8. Can the process of finding an inverse be applied to quadratic functions? Why or why not?

Tip: When solving for the inverse, always remember to interchange $x$ and $y$ and then solve for $y$. This will ensure you correctly derive the inverse function.