The equation in the image is:

$-3x - 5y = -2$

We are solving for $y$ in terms of $x$.

Steps to solve for $y$:

1. Start with the original equation: $-3x - 5y = -2$

2. Add $3x$ to both sides to isolate the $y$-term: $-5y = 3x - 2$

3. Divide both sides by $-5$ to solve for $y$: $y = \frac{3x - 2}{-5}$

4. Simplify the expression: $y = -\frac{3x}{5} + \frac{2}{5}$

So, the solution for $y$ is:

$y = -\frac{3x}{5} + \frac{2}{5}$

Would you like further details on how this was solved, or do you have any questions?

Related questions:

1. How would the solution change if the equation was $3x + 5y = 2$?
2. How can you check if a solution is correct by plugging values of $x$?
3. What happens to the equation when $x = 0$?
4. Can you solve this equation graphically, and what would the graph look like?
5. How would this problem change if the coefficients of $x$ and $y$ were different?

Tip:

When solving linear equations, remember to keep track of negative signs when isolating variables.