The question asks for the equation $2x + 6y = -12$ to be solved for $y$.

Let's solve the equation step by step:

Step 1: Isolate the $y$-term

We start by moving the $2x$ to the other side of the equation: $6y = -12 - 2x$ which can be rewritten as: $6y = -2x - 12$

Step 2: Solve for $y$

Now, divide both sides of the equation by 6 to isolate $y$: $y = \frac{-2x - 12}{6}$ Simplifying the right-hand side: $y = \frac{-2x}{6} + \frac{-12}{6}$ $y = \frac{-1}{3}x - 2$

This matches option b: $y = -\frac{1}{3}x - 2$.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you graph the equation $y = -\frac{1}{3}x - 2$?
2. What does the slope $-\frac{1}{3}$ indicate about the graph's steepness?
3. Can you rearrange other linear equations to slope-intercept form?
4. What is the y-intercept of $y = -\frac{1}{3}x - 2$, and how do you interpret it?
5. How would the equation change if the slope were positive?

Tip: When solving linear equations, aim to isolate the variable step by step, and always simplify fractions for clarity.