To solve the linear equation \( 3x + y = 6 \), there are two main approaches depending on what you need:

1. **Solve for \( y \) in terms of \( x \)**:
   \[
   y = 6 - 3x
   \]
   This is the equation in slope-intercept form (\(y = mx + b\)), where the slope \(m = -3\) and the y-intercept is \(6\).

2. **Solve for \( x \) in terms of \( y \)**:
   \[
   x = \frac{6 - y}{3}
   \]
   This gives the value of \( x \) for a given value of \( y \).

Would you like me to solve for specific values, graph this equation, or work on a system of equations with this?

### Related Questions:
1. How do you find the slope and intercept of a line from an equation?
2. What does solving for \( y \) in terms of \( x \) mean graphically?
3. How can this equation be solved in terms of inequalities?
4. How would this equation change if the constant were different, say \( 3x + y = 10 \)?
5. Can you solve this equation by substitution if paired with another?

**Tip:** When solving linear equations, putting them into slope-intercept form makes it easier to visualize their graph.

Learn how to solve the linear equation 3x + y = 6 with a detailed breakdown. Explore key algebraic concepts like slope-intercept form and methods for solving in terms of x or y. Ideal for students in Grades 6-8.

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