If \( y = x \), the values of \( y \) are identical to the values of \( x \). A table representing this linear relationship would show that for every \( x \), the corresponding \( y \) value is the same.

Here's what the table might look like:

| \( x \) | \( y \) |
|--------|--------|
| -3     | -3     |
| -2     | -2     |
| -1     | -1     |
| 0      | 0      |
| 1      | 1      |
| 2      | 2      |
| 3      | 3      |

This table shows a direct one-to-one relationship, where \( y \) equals \( x \) for all points. You can extend this table to any values of \( x \) as needed.

Would you like to explore details on how this linear function behaves graphically or algebraically? Here are some questions for further exploration:

1. What is the slope of the line represented by \( y = x \)?
2. How would the table change if the function were \( y = 2x \)?
3. How does the graph of \( y = x \) compare to other linear equations?
4. What happens if you change the equation to \( y = x + 3 \)?
5. Can this relationship be represented in terms of a real-world example?

**Tip**: The equation \( y = x \) represents a line with a slope of 1 passing through the origin (0,0).

Discover how to create a table for the linear equation y = x. This simple algebraic relationship demonstrates a one-to-one correspondence between x and y values. Learn how to build the table, understand its graphical behavior, and explore further examples. Ideal for Grades 6-8 students.

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