https://file.aiquickdraw.com/mathbot/file/1729258415994xii553uc.png

The equation provided is \( y = x \), meaning that for every value of \( x \), the corresponding value of \( y \) will be the same. Let's complete the table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 0 \\
1 & 1 \\
2 & 2 \\
3 & 3 \\
\hline
\end{array}
\]

Now, you can plot these points on the graph. The points to plot will be:

- (0, 0)
- (1, 1)
- (2, 2)
- (3, 3)

These points will form a straight line with a slope of 1, because the equation \( y = x \) represents a line with slope 1 through the origin.

Would you like any further details, or have any questions?

Here are 5 related questions to expand on this concept:

1. How would the table change if the equation was \( y = 2x \)?
2. What is the slope of the line \( y = x \) and what does it represent?
3. How would you graph the equation if it was \( y = x + 1 \)?
4. What is the general form of a linear equation and how does \( y = x \) fit into it?
5. How can you find the intersection of two lines on a graph?

**Tip:** When graphing linear equations, always check if the line passes through the origin by plugging \( x = 0 \) into the equation!

Use the equation y = x to complete the table and graph the equation.

Learn how to complete the table for the linear equation y = x and graph it on a coordinate plane. This exercise helps students understand linear relationships, proportionality, and graphing techniques, suitable for Grades 6-8.

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