What is the inverse of the equation y=3/2x

A. y=3x−2�=3�−2

B. y=−32x�=−32�

C. y=23x�=23�

D. y=x+32


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.

Learn how to find the inverse of the linear equation y = (3/2)x with step-by-step instructions. This problem covers the concept of inverse functions in algebra, suitable for students in Grades 7-9.

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