Compute for x and y coordinates x + y = 3 show step by step solution so I can create a graph.

The equation you provided is:

\[
x + y = 3
\]

This is a linear equation, and the graph will be a straight line. Let's solve it step by step for different values of \( x \) and find the corresponding \( y \) values.

### Step-by-Step Solution:

1. **Rearrange the equation to express \( y \) in terms of \( x \):**
   
   \[
   y = 3 - x
   \]

2. **Create a table of values** for different values of \( x \), and calculate the corresponding \( y \) values.

| \( x \) | \( y = 3 - x \) |
|--------|----------------|
| 0      | \( 3 - 0 = 3 \) |
| 1      | \( 3 - 1 = 2 \) |
| 2      | \( 3 - 2 = 1 \) |
| -1     | \( 3 - (-1) = 4 \) |
| -2     | \( 3 - (-2) = 5 \) |

So, the corresponding points \((x, y)\) are:
- \( (0, 3) \)
- \( (1, 2) \)
- \( (2, 1) \)
- \( (-1, 4) \)
- \( (-2, 5) \)

3. **Plot these points** on a graph. 

Now you can draw a straight line through these points to represent the equation \( x + y = 3 \).

### Steps to Graph:

1. Draw the Cartesian plane with the x-axis and y-axis.
2. Plot the points: (0, 3), (1, 2), (2, 1), (-1, 4), and (-2, 5).
3. Connect these points with a straight line.

This line represents the equation \( x + y = 3 \).

Would you like more details on how to draw the graph, or have any other questions?

### Related Questions:
1. What is the slope of the line \( x + y = 3 \)?
2. How do you find the x-intercept and y-intercept of a linear equation?
3. How would the graph change if the equation was \( x + y = 5 \)?
4. Can you write the equation in slope-intercept form?
5. How do you check if a point lies on the line of the equation \( x + y = 3 \)?

### Tip:
To graph a line easily, always find the x- and y-intercepts first by setting \( x = 0 \) and \( y = 0 \), then plot those points.

Learn how to compute x and y coordinates for the linear equation x + y = 3 and plot them on a graph with a detailed, step-by-step solution. This guide covers key algebra concepts, including rearranging equations, creating a value table, and graphing linear equations. Suitable for students in Grades 6-8.

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