The given equation is:

\[
2x + 3y = 12
\]

This is a linear equation in two variables, \(x\) and \(y\). There are several things we can do with this equation, such as:

1. **Solving for one variable in terms of the other**: We can express \(y\) in terms of \(x\) or \(x\) in terms of \(y\).
2. **Finding intercepts**: We can find the x-intercept and y-intercept by setting \(y = 0\) and \(x = 0\), respectively.
3. **Graphing the line**: This equation can be represented as a straight line on the coordinate plane.

### Let's solve for \(y\) in terms of \(x\):
\[
2x + 3y = 12
\]
Subtract \(2x\) from both sides:
\[
3y = 12 - 2x
\]
Now, divide by 3:
\[
y = \frac{12 - 2x}{3}
\]
Simplifying:
\[
y = 4 - \frac{2}{3}x
\]

This is the equation of the line in slope-intercept form \(y = mx + b\), where the slope \(m = -\frac{2}{3}\) and the y-intercept is \(4\).

Would you like more details or a graphical representation of this line?

Here are 5 related questions:
1. What is the x-intercept of this line?
2. How do we graph this equation on a coordinate plane?
3. Can we solve for \(x\) in terms of \(y\)?
4. What is the slope of this line and what does it represent?
5. How would this equation change if we added a constant to both sides?

**Tip**: To graph a line, find at least two points by setting one variable to 0 and solving for the other.

Learn how to solve the linear equation 2x + 3y = 12 and express it in slope-intercept form. Understand key concepts such as slope, y-intercept, and x-intercept. Suitable for students in Grades 8-10.

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