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To find the inverse of the equation \( y = 8x + 4 \), let's go through the steps required.

### Step-by-step solution:

1. **Start with the equation:** 
   \[
   y = 8x + 4
   \]
   
2. **Swap \(x\) and \(y\):** 
   To find the inverse, we switch \(x\) and \(y\).
   \[
   x = 8y + 4
   \]

3. **Solve for \(y\):**
   Now, we solve for \(y\), which will give us the inverse function.

   - First, subtract 4 from both sides:
     \[
     x - 4 = 8y
     \]

   - Now, divide both sides by 8:
     \[
     y = \frac{x - 4}{8}
     \]

4. **Write the inverse function:**
   The inverse of the function is:
   \[
   f^{-1}(x) = \frac{x - 4}{8}
   \]

This is the inverse of the equation \(y = 8x + 4\).

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Would you like more details or have any questions?

Here are some related questions for further practice:
1. What is the inverse of \( y = 5x + 3 \)?
2. How do you find the inverse of a quadratic function?
3. What is the significance of finding an inverse function?
4. Can all functions have inverses? Why or why not?
5. What happens to the slope in a linear function's inverse?

**Tip:** To verify if your inverse is correct, substitute the inverse function back into the original and see if you get \(x\) as the result.

Find the inverse of the following equation: y = 8x + 4

Learn how to find the inverse of the linear equation y = 8x + 4 with a step-by-step solution. This problem involves key algebraic concepts like linear equations and inverse functions. Suitable for students in Grades 9-12.

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