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:

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.