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To solve the equation \(2x + 6y = -12\) for \(y\), let's follow these steps:

1. **Isolate the term with \(y\):**

   Subtract \(2x\) from both sides:
   \[
   6y = -2x - 12
   \]

2. **Solve for \(y\):**

   Divide every term by 6 to isolate \(y\):
   \[
   y = \frac{-2x - 12}{6}
   \]

3. **Simplify the equation:**

   Simplify each term:
   \[
   y = \frac{-2x}{6} - \frac{12}{6}
   \]
   \[
   y = -\frac{1}{3}x - 2
   \]

This corresponds to option **(b) \(y = -2x - 2\)**, which looks different but is not simplified correctly. The equation obtained is:

   \[
   y = -\frac{1}{3}x - 2
   \]

Unfortunately, none of the provided options match exactly after the complete simplification.

Would you like more details on this or further assistance with another problem?

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**Relative Questions:**
1. What does it mean to "solve for \(y\)" in an equation?
2. How do you isolate a variable in a linear equation?
3. How can simplifying fractions in algebraic expressions help solve equations?
4. Why is it important to check your answer against the original equation?
5. What is the difference between solving equations in standard form and slope-intercept form?

**Tip:** Always double-check the options given in multiple-choice questions after solving to ensure proper simplification and matching with choices.

Which of the following shows the equation solved for y? 2x + 6y = -12

Learn how to solve for y in the linear equation 2x + 6y = -12. This guide walks through the process of isolating y and simplifying the equation. Suitable for students in Grades 6-8.

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