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

### Step 1: Isolate the term involving \( y \)
Subtract \( 6x \) from both sides of the equation:
\[
2y = 12 - 6x
\]

### Step 2: Solve for \( y \)
Divide both sides of the equation by 2 to solve for \( y \):
\[
y = \frac{12 - 6x}{2}
\]

Simplify the right-hand side:
\[
y = 6 - 3x
\]

So, the solution is:
\[
y = 6 - 3x
\]

Would you like further details or clarifications?

Here are 5 related questions:
1. How would you graph \( y = 6 - 3x \)?
2. What is the slope and y-intercept of the line \( y = 6 - 3x \)?
3. How do you solve the equation \( 6x + 2y = 12 \) for \( x \)?
4. Can this equation represent a system of equations if paired with another one?
5. What are the solutions for specific values of \( x \), like \( x = 2 \) or \( x = -1 \)?

**Tip:** Always check your solution by plugging it back into the original equation to verify its correctness.

This guide explains how to solve the linear equation 6x + 2y = 12 for y in a step-by-step approach. Key algebra concepts, such as isolating variables and simplifying expressions, are covered. Suitable for students in Grades 7-9.

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