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 $y = 8x + 4$.

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.