https://file.aiquickdraw.com/mathbot/file/1727926682680laybv9x1.jpg

The image shows a table that corresponds to the equation \( x + 2y = 6 \), with a request to complete the table and graph the equation.

The table has two entries:
- When \( x = 0 \), \( y = 3 \) is provided.
- When \( y = 0 \), we need to find \( x \).

Let's solve for \( x \) when \( y = 0 \):

Given the equation:
\[
x + 2y = 6
\]

Substitute \( y = 0 \):
\[
x + 2(0) = 6
\]
\[
x = 6
\]

Now, we can complete the table:
- When \( x = 0 \), \( y = 3 \) (already given).
- When \( y = 0 \), \( x = 6 \).

The completed table looks like this:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 3 \\
6 & 0 \\
\hline
\end{array}
\]

For the graph, you can plot the points \( (0, 3) \) and \( (6, 0) \), and draw a straight line through these points to represent the equation.

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

Here are 5 related questions you might want to explore:
1. How do you determine the slope of a line from two points?
2. What are the intercepts of the line, and what do they represent?
3. How would you rewrite the equation \( x + 2y = 6 \) in slope-intercept form?
4. What is the significance of solving for \( y \) when \( x = 0 \) and vice versa?
5. How can you use a graph to verify the solution of an equation?

**Tip**: When graphing linear equations, always find at least two points and draw a line through them. This ensures accuracy when representing the equation visually.

Complete the table for the equation x + 2y = 6, and graph the equation.

This exercise involves solving the linear equation x + 2y = 6 by completing a table and graphing the equation. Key algebraic concepts are covered, including solving for variables and plotting points. Suitable for Grades 6-8.

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