To complete the table using the rule $2x + y = 16$, we'll substitute the given values of $x$ into the equation and solve for $y$.

1. When $x = 1$: 2 + y = 16 \\ y = 16 - 2 = 14$$
2. When $x = 2$: 4 + y = 16 \\ y = 16 - 4 = 12$$
3. When $x = 4$: 8 + y = 16 \\ y = 16 - 8 = 8$$
4. When $x = 6$: 12 + y = 16 \\ y = 16 - 12 = 4$$
5. When $x = 8$: 16 + y = 16 \\ y = 16 - 16 = 0$$

Now, we can complete the table:

x & 1 & 2 & 4 & 6 & 8 \\ \hline y & 14 & 12 & 8 & 4 & 0 \\ \end{array}$$ Would you like any further details or explanations on this problem? Here are some related questions to explore: 1. How would the equation change if the rule was $$2x + y = 20$$? 2. What happens to the values of $$y$$ if $$x$$ is negative? 3. How can you graph the equation $$2x + y = 16$$? 4. What if the equation was $$3x + y = 16$$? How would the table change? 5. How do you interpret the relationship between $$x$$ and $$y$$ from the equation? 6. How would you solve for $$x$$ if $$y$$ was given instead? 7. What is the slope of the line represented by $$2x + y = 16$$? 8. How does the equation $$2x + y = 16$$ relate to real-world scenarios? **Tip:** When solving for a variable, always isolate it on one side of the equation by performing inverse operations.