To solve this problem and complete the table for $y = \frac{1}{2}x + 1$, we will substitute the given $x$-values into the equation and calculate $y$.

1. For $x = -4$: $y = \frac{1}{2}(-4) + 1 = -2 + 1 = -1$

2. For $x = -2$: $y = \frac{1}{2}(-2) + 1 = -1 + 1 = 0$

3. For $x = 0$: $y = \frac{1}{2}(0) + 1 = 0 + 1 = 1$

4. For $x = 6$: $y = \frac{1}{2}(6) + 1 = 3 + 1 = 4$

5. For $x = 8$: $y = \frac{1}{2}(8) + 1 = 4 + 1 = 5$

Completed Table:

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Related Questions:

1. How do you determine the slope of a linear function from its equation?
2. What does the $y$-intercept represent in this equation?
3. How can you verify the points are correct for the given equation?
4. How does increasing the slope affect the steepness of the graph?
5. What is the significance of the $x$- and $y$-intercepts?

Tip:

When completing a table for a linear function, always calculate at least three points to confirm the line is correct and plot the graph accurately.