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.





Let's complete the table and then discuss how to graph the function \( y = -\frac{1}{2}x - 5 \).

### Step 1: Calculate the \( y \)-values

Given the function \( y = -\frac{1}{2}x - 5 \):

- When \( x = -10 \):
  \[
  y = -\frac{1}{2}(-10) - 5 = 5 - 5 = 0
  \]
  
- When \( x = -4 \):
  \[
  y = -\frac{1}{2}(-4) - 5 = 2 - 5 = -3
  \]

- When \( x = 0 \):
  \[
  y = -\frac{1}{2}(0) - 5 = 0 - 5 = -5
  \]

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

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

### Completed Table

\[
\begin{array}{c|c}
x & y \\
\hline
-10 & 0 \\
-4 & -3 \\
0 & -5 \\
8 & -9 \\
10 & -10 \\
\end{array}
\]

### Step 2: Graph the Function

The points to plot on the graph are:
- \( (-10, 0) \)
- \( (-4, -3) \)
- \( (0, -5) \)
- \( (8, -9) \)
- \( (10, -10) \)

These points will form a straight line, as the function is linear with a slope of \(-\frac{1}{2}\).

To graph:
1. Plot each of the points on a coordinate plane.
2. Draw a straight line that passes through all the plotted points.

Would you like further details on how to plot the points, or do you have any other questions?

### Related Questions:
1. What does the slope of \(-\frac{1}{2}\) indicate about the direction of the line?
2. How do you find the \(x\)-intercept of the function \(y = -\frac{1}{2}x - 5\)?
3. What is the significance of the \(y\)-intercept in this function?
4. How would the graph change if the function were \(y = \frac{1}{2}x - 5\) instead?
5. How do you graph a function if given only the slope and \(y\)-intercept?

**Tip:** When working with linear equations, identifying the slope and intercepts can help you quickly sketch the graph.

Learn how to complete the table and graph the function y = -1/2x - 5 step-by-step with detailed calculations and plotted points. This problem covers linear equations and graphing functions, suitable for students in Grades 7-9.

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