https://file.aiquickdraw.com/mathbot/file/1730556809608wrdm97sr.jpg

To find the values of \( A \), \( B \), and \( C \) in the table, we need to use the equation given for the graph:

\[
x + y = 6
\]

We can solve for \( y \) in terms of \( x \) by rearranging the equation:

\[
y = 6 - x
\]

Now we substitute each given \( x \)-value into this equation to find the corresponding \( y \)-values.

### 1. Find \( A \) when \( x = -2 \):
\[
y = 6 - (-2) = 6 + 2 = 8
\]
So, \( A = 8 \).

### 2. Check the value of \( B \) when \( x = 0 \):
\[
y = 6 - 0 = 6
\]
So, \( B = 6 \).

### 3. Find \( C \) when \( x = 2 \):
\[
y = 6 - 2 = 4
\]
So, \( C = 4 \).

### Completed Table:
| \( x \) | -2 | -1 |  0 |  1 |  2 |
|---------|----|----|----|----|----|
| \( y \) |  8 |  7 |  6 |  5 |  4 |

The values that should replace \( A \), \( B \), and \( C \) are:
- \( A = 8 \)
- \( B = 6 \)
- \( C = 4 \)

Would you like more details on any of the steps?

### Related Questions:
1. How would you graph this equation based on the table values?
2. What is the slope and y-intercept of the equation \( x + y = 6 \)?
3. How would the table change if the equation were \( x + y = 10 \)?
4. Can this table help us find points for graphing other lines? If so, how?
5. How do you determine the intercepts of the line \( x + y = 6 \)?

### Tip:
When given an equation, solving for one variable in terms of the other can help you quickly generate points to plot its graph.

Copy and complete the table below for the graph of x + y = 6. What values should replace A and B?

Learn how to complete a table of values for the equation x + y = 6. This problem demonstrates how to use algebra to find corresponding y-values for given x-values, suitable for students in Grades 6-8.

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