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.

Explore the linear equation x + y = 3 with detailed explanations on graphical representation, slope-intercept form, and solving techniques. Learn how to graph the line, find intersections, and apply the equation in real-world scenarios. Suitable for students in Grades 7-9.

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