To solve the equation \( \frac{1}{3}x + 2y = 8 \) for \( y \), follow these steps:

### Step 1: Subtract \( \frac{1}{3}x \) from both sides
\[
2y = 8 - \frac{1}{3}x
\]

### Step 2: Multiply both sides by \( \frac{1}{2} \) to isolate \( y \)
\[
y = \frac{1}{2} \left(8 - \frac{1}{3}x \right)
\]

### Step 3: Distribute the \( \frac{1}{2} \)
\[
y = \frac{1}{2}(8) - \frac{1}{2} \left( \frac{1}{3}x \right)
\]
\[
y = 4 - \frac{1}{6}x
\]

Thus, the solution for \( y \) is:
\[
y = 4 - \frac{1}{6}x
\]

Would you like more details on any part of the solution? 

Here are 5 related questions:
1. How would you graph the equation \( y = 4 - \frac{1}{6}x \)?
2. What is the slope and y-intercept of the equation in slope-intercept form?
3. How do you solve for \( x \) in a similar linear equation?
4. What happens to the equation when \( x = 0 \)?
5. How do you convert this equation into standard form?

**Tip:** When isolating a variable, always move terms without the variable first before dividing or multiplying to simplify.

Learn how to solve the linear equation 1/3x + 2y = 8 for y using algebraic techniques. This step-by-step guide demonstrates how to isolate variables, apply the distributive property, and express the equation in slope-intercept form. Suitable for students in Grades 8-10.

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