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The problem asks to complete the table for the equation \( x + 2y = 1 \) and to graph the equation.

Let's break down the equation and solve for \( y \) in terms of \( x \):

\[
x + 2y = 1
\]
\[
2y = 1 - x
\]
\[
y = \frac{1 - x}{2}
\]

Now, using this equation, let's find the missing values for \( y \) corresponding to the given \( x \) values in the table:

1. When \( x = 0 \):
   \[
   y = \frac{1 - 0}{2} = \frac{1}{2} = 0.5
   \]
   (This value is already given as 0.5.)

2. When \( x = 1 \):
   \[
   y = \frac{1 - 1}{2} = \frac{0}{2} = 0
   \]
   (This value is already given as 0.)

3. When \( x = 6 \):
   \[
   y = \frac{1 - 6}{2} = \frac{-5}{2} = -2.5
   \]
   (This value is also given as -2.5.)

So the table is complete with the correct values. To graph the equation, you can plot these points: 
- \( (0, 0.5) \)
- \( (1, 0) \)
- \( (6, -2.5) \)

The graph will be a straight line passing through these points since it's a linear equation.

Do you have any questions or want more details about the graphing process?

Here are some related questions:
1. What is the slope of the line represented by the equation \( x + 2y = 1 \)?
2. How do you find the x-intercept and y-intercept of a linear equation?
3. How can you convert a general linear equation into slope-intercept form?
4. What are the different ways to graph a linear equation without using a table of values?
5. How does changing the coefficient of \( y \) in the equation affect the graph's slope?

**Tip:** When graphing linear equations, it helps to find both intercepts (x and y) first. This gives you two easy points to start the graph.

Complete the table for the equation x + 2y = 1, and graph the equation.

Learn how to complete the table and graph the linear equation x + 2y = 1. This problem covers algebraic concepts such as solving for y and plotting points for a straight-line graph. Suitable for students in Grades 8-10.

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