To complete the table and graph the function for $y = -\frac{1}{2}x - 5$, we will first fill in the values for $y$ using the given $x$ values, and then plot these points on a graph.

Step 1: Complete the Table

The function given is $y = -\frac{1}{2}x - 5$.

For each $x$ value, calculate the corresponding $y$ value using the formula:

1. When $x = -10$: $y = -\frac{1}{2}(-10) - 5 = 5 - 5 = 0$

2. When $x = -4$: $y = -\frac{1}{2}(-4) - 5 = 2 - 5 = -3$

3. When $x = 0$: $y = -\frac{1}{2}(0) - 5 = 0 - 5 = -5$

4. When $x = 8$: $y = -\frac{1}{2}(8) - 5 = -4 - 5 = -9$

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

Completed Table:

$x$	$y$
-10	0
-4	-3
0	-5
8	-9
10	-10

Step 2: Plot the Points on a Graph

• Plot the points $(-10, 0)$, $(-4, -3)$, $(0, -5)$, $(8, -9)$, and $(10, -10)$ on a Cartesian coordinate plane.
• Draw a line through these points to represent the linear function $y = -\frac{1}{2}x - 5$.

Graph:

1. On the x-axis, mark points from $-10$ to $10$.
2. On the y-axis, mark points from $0$ to $-10$.
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 $y = -\frac{1}{2}x - 5$?
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 positive?
4. What is the x-intercept of this function, and how is it calculated?
5. How can this linear function be used to model real-world scenarios?

Tip: When graphing linear equations, the slope indicates how steep the line is, and the y-intercept indicates where the line crosses the y-axis.