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The equation provided is \( y = -2x - 1 \). You are asked to complete the table with missing values for \( y \) corresponding to different values of \( x \).

Let's substitute the given \( x \) values into the equation \( y = -2x - 1 \) to find the missing values:

1. For \( x = -2 \):
   \[
   y = -2(-2) - 1 = 4 - 1 = 3
   \]
   So the value for \( y \) when \( x = -2 \) is 3, which matches the table.

2. For \( x = -1 \) (finding A):
   \[
   y = -2(-1) - 1 = 2 - 1 = 1
   \]
   So, \( A = 1 \).

3. For \( x = 0 \) (finding B):
   \[
   y = -2(0) - 1 = 0 - 1 = -1
   \]
   So, \( B = -1 \).

4. For \( x = 1 \):
   \[
   y = -2(1) - 1 = -2 - 1 = -3
   \]
   This matches the table.

5. For \( x = 2 \) (finding C):
   \[
   y = -2(2) - 1 = -4 - 1 = -5
   \]
   So, \( C = -5 \).

The completed table is:
\[
\begin{array}{c|c|c|c|c|c|c}
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & 3 & 1 & -1 & -3 & -5 \\
\end{array}
\]

Do you want any further details or clarifications?

Here are five related questions to deepen your understanding:
1. What is the slope of the graph \( y = -2x - 1 \)?
2. How would you graph this equation based on the table of values?
3. What is the y-intercept of the equation \( y = -2x - 1 \)?
4. How does changing the slope affect the graph of a line?
5. What happens to the graph if the constant term changes from \(-1\) to a different value?

**Tip**: The slope of the equation tells you how much \( y \) changes for each unit change in \( x \).

Copy and complete the table for the graph y = -2x - 1. What values should replace A, B, and C?

Learn how to complete a table for the linear equation y = -2x - 1 by substituting values of x to find corresponding y values. This problem involves understanding linear equations and substitution methods, suitable for students in Grades 6-8.

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