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To complete this table using the function \( y = -2x + 4 \), we will substitute each \( x \)-value into the equation to solve for \( y \).

1. For \( x = -6 \):
   \[
   y = -2(-6) + 4 = 12 + 4 = 16
   \]

2. For \( x = -3 \):
   \[
   y = -2(-3) + 4 = 6 + 4 = 10
   \]

3. For \( x = 0 \):
   \[
   y = -2(0) + 4 = 0 + 4 = 4
   \]

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

So, the completed table is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & 16 \\
-3 & 10 \\
0 & 4 \\
3 & -2 \\
\hline
\end{array}
\]

Would you like more details on the calculations or have any questions?

Here are some related questions for further exploration:
1. What happens to the \( y \)-values if the slope is changed from \(-2\) to another value?
2. How does the \( y \)-intercept affect the values in the table?
3. Can you identify the pattern in \( y \)-values as \( x \) increases?
4. What would the table look like if the function were \( y = 2x + 4 \) instead?
5. How can you use this table to plot points on a graph?

**Tip:** When substituting values, work step-by-step to avoid errors, especially with negative signs!

Fill in the table using the function rule y = -2x + 4

Learn how to complete a table of values using the linear function y = -2x + 4. This example demonstrates substitution of values to find corresponding y-values, suitable for students in Grades 7-9.

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