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We are given the linear equation \( y = -3x - 2 \), and we need to complete the table of values for different \( x \)-values.

The equation tells us that for any value of \( x \), we can calculate \( y \) by substituting the value of \( x \) into the equation \( y = -3x - 2 \).

Let's calculate the values for each \( x \) in the table:

1. For \( x = -3 \):
   \[
   y = -3(-3) - 2 = 9 - 2 = 7
   \]

2. For \( x = 0 \):
   \[
   y = -3(0) - 2 = 0 - 2 = -2
   \]

3. For \( x = 3 \):
   \[
   y = -3(3) - 2 = -9 - 2 = -11
   \]

4. For \( x = 6 \):
   \[
   y = -3(6) - 2 = -18 - 2 = -20
   \]

Now, the completed table is:

\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -3 & 0 & 3 & 6 \\
\hline
y & 7 & -2 & -11 & -20 \\
\hline
\end{array}
\]

Would you like a more detailed explanation of any step? Here are some related questions to explore:

1. How do you graph the equation \( y = -3x - 2 \)?
2. What is the slope and y-intercept of the equation \( y = -3x - 2 \)?
3. How would the table change if the equation was \( y = 3x - 2 \)?
4. How do we determine if a line is increasing or decreasing from its equation?
5. What happens to the y-values if you increase the x-values in the equation \( y = -3x - 2 \)?

**Tip:** To quickly find values for linear equations, remember to calculate the slope first and apply it consistently across all x-values.

Consider the equation y = -3x - 2. Fill in the blanks to complete the table of values.

Learn how to fill in the table of values for the linear equation y = -3x - 2 using substitution. This problem covers essential algebraic concepts suitable for students in Grades 6-8.

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