To complete the table for the function $y = \frac{1}{2}x + 11$ and then graph the function, we'll calculate the corresponding $y$ values for each given $x$ value.

Step 1: Complete the Table

The function given is $y = \frac{1}{2}x + 11$.

1. When $x = -10$: $y = \frac{1}{2}(-10) + 11 = -5 + 11 = 6$

2. When $x = -8$: $y = \frac{1}{2}(-8) + 11 = -4 + 11 = 7$

3. When $x = -4$: $y = \frac{1}{2}(-4) + 11 = -2 + 11 = 9$

4. When $x = -2$: $y = \frac{1}{2}(-2) + 11 = -1 + 11 = 10$

Completed Table:

Step 2: Plot the Points on a Graph

• Plot the points $(-10, 6)$, $(-8, 7)$, $(-4, 9)$, and $(-2, 10)$ on a Cartesian coordinate plane.
• Draw a line through these points to represent the linear function $y = \frac{1}{2}x + 11$.

Graph:

1. On the x-axis, mark points from $-10$ to $0$ (and beyond if needed).
2. On the y-axis, mark points from $0$ to $10$ (and beyond if needed).
3. Plot the calculated points and connect them to form the line.

Would you like any further details or have any questions about the graph?

Related Questions:

1. How do you find the slope of the line from the equation $y = \frac{1}{2}x + 11$?
2. What is the y-intercept of the line, and what does it represent in this context?
3. How would the graph change if the slope were negative?
4. What is the x-intercept of this function, and how is it calculated?
5. How does the line's slope affect its steepness?

Tip: A positive slope means the line rises as $x$ increases, while a negative slope means it falls.