Question

give me a table an a graph of a proportional relantionship

Answer 1

Certainly! A proportional relationship is one where two quantities increase or decrease at the same rate, which can be represented as \(y = kx\), where \(k\) is the constant of proportionality.

### Table of Proportional Relationship
Let’s consider the relationship between hours worked (x) and earnings (y) where you earn $15 per hour (constant of proportionality \(k = 15\)).

| Hours Worked (x) | Earnings (y) |
|------------------|--------------|
| 0 | 0 |
| 1 | 15 |
| 2 | 30 |
| 3 | 45 |
| 4 | 60 |
| 5 | 75 |
| 6 | 90 |
| 7 | 105 |
| 8 | 120 |

### Graph of the Proportional Relationship

To graph this relationship, plot the data points from the table on a coordinate system, where the x-axis represents Hours Worked and the y-axis represents Earnings. The graph should be a straight line passing through the origin (0,0) with a slope equal to the constant of proportionality (15 in this case).

Here’s a description of how you might visualize the graph if you were drawing it:

1. **Plot the Points**:
- Plot points for each (x, y) pair from the table.
- For example: (0, 0), (1, 15), (2, 30), ..., (8, 120).

2. **Draw the Line**:
- Connect all the points with a straight line.
- Since it is a proportional relationship, the line will pass through the origin and have a positive slope.

### Example Graph Sketch (Text-Based)

```
Earnings
120 | *
|
90 | *
|
60 | *
|
30 | *
|
0 |___________________________
0 1 2 3 4 5 Hours Worked
```

You can plot this graph using graphing software or graph paper for a more precise representation. Let me know if you need further assistance!