The equation given is:

\[
2x + 3y = 12
\]

This is a linear equation in two variables, \(x\) and \(y\). You can solve this equation for one variable in terms of the other, or if given additional information (like another equation), you could solve for both \(x\) and \(y\).

### Solving for \(y\) in terms of \(x\):

\[
3y = 12 - 2x
\]

Now, divide by 3:

\[
y = \frac{12 - 2x}{3}
\]

This simplifies to:

\[
y = 4 - \frac{2}{3}x
\]

Thus, \(y\) is expressed in terms of \(x\).

### Solving for \(x\) in terms of \(y\):

\[
2x = 12 - 3y
\]

Now, divide by 2:

\[
x = \frac{12 - 3y}{2}
\]

This simplifies to:

\[
x = 6 - \frac{3}{2}y
\]

Thus, \(x\) is expressed in terms of \(y\).

Would you like more details on how to graph this or solve it further with specific values?

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Here are five related questions:
1. How do you graph the equation \(2x + 3y = 12\) on a coordinate plane?
2. What are the intercepts of the equation \(2x + 3y = 12\)?
3. How do you find the slope of a line from the equation \(2x + 3y = 12\)?
4. How would you solve this equation if given a second equation in a system?
5. What happens if you substitute specific values for \(x\) or \(y\)?

**Tip:** A linear equation can always be rewritten in slope-intercept form \(y = mx + b\), which makes it easier to understand the slope and y-intercept of the line.

Explore the solution to the linear equation 2x + 3y = 12, including solving for y in terms of x and vice versa. This guide covers key algebra concepts such as linear equations, slope-intercept form, and system solving techniques. Suitable for students in Grades 6-8.

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