Question

Graph proportional relationships

Answer 1

Graphing proportional relationships involves plotting points on a coordinate system to represent the relationship between two quantities that vary proportionally. Here's a step-by-step guide to help you understand how to graph a proportional relationship:

### Steps to Graph a Proportional Relationship

1. **Understand the Definition**:
A proportional relationship can be expressed in the form \( y = kx \), where \( k \) is the constant of proportionality. In this relationship, if you double \( x \), \( y \) also doubles.

2. **Choose Values for \( x \)**:
Select a range of values for \( x \). These values can be any real numbers, but they should be evenly spaced (e.g., 0, 1, 2, 3, 4...).

3. **Calculate Corresponding \( y \) Values**:
Use the formula \( y = kx \) to calculate the corresponding \( y \) values based on your chosen \( x \) values. For example, if \( k = 2 \) and you choose \( x \) values of 0, 1, 2, 3, 4, then \( y \) values would be:
- If \( x = 0 \), then \( y = 2(0) = 0 \)
- If \( x = 1 \), then \( y = 2(1) = 2 \)
- If \( x = 2 \), then \( y = 2(2) = 4 \)
- If \( x = 3 \), then \( y = 2(3) = 6 \)
- If \( x = 4 \), then \( y = 2(4) = 8 \)

4. **Create a Table**:
Organize your \( x \) and \( y \) values in a table:

| \( x \) | \( y \) |
|---------|---------|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

5. **Plot the Points**:
On a coordinate plane, plot the points corresponding to your table. For our example, you would plot the points (0,0), (1,2), (2,4), (3,6), and (4,8).

6. **Draw the Line**:
Since the relationship is linear (a straight line), draw a straight line through the points. The line should pass through the origin (0,0) because a proportional relationship always includes this point.

7. **Label the Graph**:
Finally, label your axes (usually \( x \) on the horizontal axis and \( y \) on the vertical axis) and give your graph a title to indicate what it represents.

### Example

For a proportional relationship where \( k = 2 \):
- \( y = 2x \) creates a straight line that can be graphed as described.

### Key Characteristics of Proportional Relationships

- **Origin**: The graph will always pass through the origin (0,0).
- **Straight Line**: The graph will be a straight line.
- **Constant Slope**: The slope of the line is equal to the constant \( k \).

### Conclusion
By following these steps, you can graph any proportional relationship effectively. If you have a specific equation or values you'd like to use, feel free to share!