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.