The given equation is:

\[
2x + 3y = 6
\]

This is a linear equation in two variables, \(x\) and \(y\). There are different ways to approach solving or interpreting it, depending on the task at hand.

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

To express \(y\) as a function of \(x\), solve the equation for \(y\):

\[
3y = 6 - 2x
\]

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

Simplifying further:

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

This gives the equation of a line with slope \(-\frac{2}{3}\) and y-intercept \(2\).

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

Similarly, solving for \(x\) in terms of \(y\):

\[
2x = 6 - 3y
\]

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

Simplifying:

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

### 3. Graphical Interpretation:
The equation represents a straight line in the Cartesian plane. You can plot the points by substituting values for \(x\) or \(y\) and finding the corresponding values of the other variable.

For example:
- If \(x = 0\), \(y = 2\)
- If \(y = 0\), \(x = 3\)

These points (\(0,2\) and \(3,0\)) are on the line.

Would you like further explanation or more details on this? Feel free to ask!

Here are some related questions:
1. What is the slope and y-intercept of the line?
2. How do you find the x-intercept and y-intercept of the equation?
3. What are the solutions of this equation when \(x = 1\)?
4. How can this equation be written in standard form?
5. How would you graph this equation?

**Tip:** To quickly find the x- and y-intercepts of a linear equation, set one variable to 0 and solve for the other.

Learn how to solve the linear equation 2x + 3y = 6 by finding the slope and intercept. This tutorial covers graphing linear equations, determining x- and y-intercepts, and understanding the slope-intercept form. Perfect for students in Grades 8-10.

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