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To complete the table for the equation \( y = -2x \), let's substitute each \( x \)-value into the equation to find the corresponding \( y \)-values.

1. When \( x = -1 \):
   \[
   y = -2(-1) = 2
   \]

2. When \( x = 0 \):
   \[
   y = -2(0) = 0
   \]

3. When \( x = 1 \):
   \[
   y = -2(1) = -2
   \]

4. When \( x = 2 \):
   \[
   y = -2(2) = -4
   \]

Now, the completed table of values is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & 2 \\
0 & 0 \\
1 & -2 \\
2 & -4 \\
\hline
\end{array}
\]

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

Here are some related questions to deepen your understanding:

1. What happens to the values of \( y \) as \( x \) increases in this equation?
2. How would the values change if the equation was \( y = 2x \) instead of \( y = -2x \)?
3. What is the slope of the line represented by this equation, and how can you tell?
4. How would you plot these points on a graph, and what shape would the line take?
5. How would this table look if \( y = -2x + 3 \) instead?

**Tip:** Remember, in a linear equation like \( y = -2x \), the coefficient of \( x \) represents the slope of the line.

Consider the equation y = -2x. Fill in the blanks to complete the table of values.

Complete the table for the linear equation y = -2x by substituting values for x and finding the corresponding values of y. This exercise helps students understand graphing, substitution, and linear relationships.

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