The equation you provided is:

\[
6x + 2y = 32
\]

We can solve this equation in several ways depending on what you're looking for. Do you want to solve for \(x\), \(y\), or express one variable in terms of the other? 

Let’s solve for \(y\) in terms of \(x\):

### Step-by-Step Solution:
1. Start with the equation:
   \[
   6x + 2y = 32
   \]

2. Subtract \(6x\) from both sides:
   \[
   2y = 32 - 6x
   \]

3. Divide both sides by 2 to isolate \(y\):
   \[
   y = \frac{32 - 6x}{2}
   \]

4. Simplify:
   \[
   y = 16 - 3x
   \]

So, the solution for \(y\) in terms of \(x\) is:

\[
y = 16 - 3x
\]

Would you like to see other methods, such as solving for \(x\), or exploring this further?

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Here are 5 related questions:
1. How would you solve for \(x\) in terms of \(y\)?
2. What happens if we set specific values for \(x\)? What are the corresponding \(y\) values?
3. How would the graph of this equation look like in the coordinate plane?
4. Can you convert this equation into slope-intercept form \(y = mx + b\) and identify the slope and y-intercept?
5. What are the intercepts of the line formed by this equation?

**Tip**: When solving for a variable, always ensure you isolate it on one side of the equation by performing inverse operations step by step.

Learn how to solve the linear equation 6x + 2y = 32 by isolating y in terms of x. This step-by-step solution simplifies the equation to the form y = 16 - 3x, covering algebraic concepts and operations suitable for students in Grades 7-9.

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