The equation $x + y = 3$ represents a line in a two-dimensional plane. This line consists of all the points $(x, y)$ that satisfy the equation. Here are a few ways to interpret and work with this equation:

1. Graphical Representation: You can graph this line by finding two points that satisfy the equation and then drawing a line through them. For example:

   • When $x = 0$, $y = 3$. So, the point $(0, 3)$ is on the line.
   • When $y = 0$, $x = 3$. So, the point $(3, 0)$ is on the line.

2. Solving for $y$: You can express $y$ in terms of $x$: $y = 3 - x$ This is the slope-intercept form of the line, $y = mx + b$, where the slope $m = -1$ and the y-intercept $b = 3$.

3. Solving for $x$: Similarly, you can express $x$ in terms of $y$: $x = 3 - y$

4. Finding Intersections: If you have another equation, you can find the intersection point by solving the system of equations.

5. Applications: This type of linear equation can be used to model real-world scenarios where two quantities add up to a constant value.

Would you like more details or have any specific questions about this equation?

Here are five questions you might find interesting:

1. How do you solve a system of linear equations involving $x + y = 3$?
2. What are the properties of the line represented by $x + y = 3$?
3. How can you find the distance from a point to the line $x + y = 3$?
4. What is the slope of the line $x + y = 3$ and how does it affect its graph?
5. How can you determine if a point lies on the line $x + y = 3$?

Tip: When working with linear equations, always try to rewrite the equation in the slope-intercept form $y = mx + b$ to easily identify the slope and y-intercept.