Complete the table and then graph the function.
y=–
1

2
x–5
x	y
–
10
–
4
0
8
10
Click to select points on the graph.

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.

Learn how to complete the table and graph the linear function y = -1/2x - 5 step-by-step. This problem involves calculating values of y for given x, plotting points, and graphing a linear function. Suitable for students in Grades 7-9.

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