The equation in the image is:

$-8y + 1 = -9y$

Steps to solve for $y$:

1. Add $9y$ to both sides to eliminate the $-9y$ on the right-hand side:

$-8y + 9y + 1 = -9y + 9y$

This simplifies to:

$y + 1 = 0$

2. Subtract 1 from both sides to isolate $y$:

$y = -1$

Thus, the solution is $y = -1$.

Would you like any further explanation or details?

Related questions:

1. How do you check if the solution is correct?
2. What happens if the equation involves more complex terms?
3. Can this process be applied to equations with fractions?
4. What are the common mistakes when solving linear equations?
5. How does this type of equation change if the coefficients of $y$ are positive?

Tip: When solving equations, always perform the same operation on both sides to maintain equality!