Question

Complete the table and then graph the function.
y=1/2 x –5

x y
–10
–2
0
6

Answer 1

Let's complete the table using the equation \( y = \frac{1}{2}x - 5 \).

We will calculate \( y \) for each \( x \) value provided:

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

2. For \( x = -2 \):
\[
y = \frac{1}{2}(-2) - 5 = -1 - 5 = -6
\]

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

4. For \( x = 6 \):
\[
y = \frac{1}{2}(6) - 5 = 3 - 5 = -2
\]

Now we have:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-10 & -10 \\
-2 & -6 \\
0 & -5 \\
6 & -2 \\
\hline
\end{array}
\]

### Table Completion

So the completed table is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-10 & -10 \\
-2 & -6 \\
0 & -5 \\
6 & -2 \\
\hline
\end{array}
\]

### Graphing the Function

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

1. Plot the points from the table:
- Point 1: \((-10, -10)\)
- Point 2: \((-2, -6)\)
- Point 3: \((0, -5)\)
- Point 4: \((6, -2)\)

2. Draw a straight line through the points, since this is a linear function.

The slope of the line is \( \frac{1}{2} \), meaning for every 2 units you move in the x direction, you move up 1 unit in the y direction.

**Graphing Instructions:**
- Start at the y-intercept, which is \( (0, -5) \).
- From there, use the slope to find other points.
- Draw the line that connects the points, and continue it in both directions.

This graph will represent the linear function \( y = \frac{1}{2}x - 5\). If you need a specific visual graph, please use graphing software or graph paper to plot the points and the line.