Question

Complete the table and then graph
y=1/9x-1

x y
-9 ?
0 ?
9 9

Answer 1

To complete the table for the equation \( y = \frac{1}{9}x - 1 \), we will calculate the \( y \) values for the given \( x \) values.

1. **For \( x = -9 \)**:
\[
y = \frac{1}{9}(-9) - 1 = -1 - 1 = -2
\]

2. **For \( x = 0 \)**:
\[
y = \frac{1}{9}(0) - 1 = 0 - 1 = -1
\]

3. **For \( x = 9 \)** (already given):
\[
y = 9
\]

Now, we can fill in the table:

| x | y |
|----|----|
| -9 | -2 |
| 0 | -1 |
| 9 | 9 |

### Graphing the Equation

Now that we have the complete table, we can graph the points:

- Point (-9, -2)
- Point (0, -1)
- Point (9, 9)

### Steps to Graph:
1. Plot the points on the Cartesian plane.
2. Draw a straight line through the points.

The equation \( y = \frac{1}{9}x - 1 \) indicates that the slope is \( \frac{1}{9} \), which means for every increase of 9 in \( x \), \( y \) increases by 1. The \( y \)-intercept is at \( (0, -1) \).

### Graph Representation:
Due to the limitations of plain text, I'll describe how to visualize it:
- Draw a horizontal axis (x-axis) and a vertical axis (y-axis).
- Mark the points (-9, -2), (0, -1), and (9, 9).
- Draw a straight line connecting these points, extending beyond in both directions.

The line will have a gentle upward slope due to the small slope \( \frac{1}{9} \).

If you would like help with anything else or more detailed graphing steps, let me know!