Question

Graph proportional relationships quick check

Answer 1

To quickly assess your understanding of graphing proportional relationships, consider the following steps:

### Key Concepts:
1. **Proportional Relationship:** A relationship between two quantities where their ratio is constant.
2. **Graphing:** In a graph of a proportional relationship, a straight line passes through the origin (0,0).

### Steps for Graphing:
1. **Identify the Variables:** Choose the two quantities you are comparing (e.g., distance vs. time).
2. **Create a Table:** List pairs of proportional values. For example, if \( y = kx \) where \( k \) is the constant of proportionality:
- If \( k = 2 \): \( (0,0), (1,2), (2,4), (3,6) \).
3. **Plot the Points:** On a graph, plot the points you've created.
4. **Check for Linearity:** The points should form a straight line that passes through the origin.
5. **Draw the Line:** Connect the points with a straight line extending in both directions.

### Example:
- Given \( y = 3x \): Create pairs like (0, 0), (1, 3), (2, 6), (3, 9).
- Plot these points on a graph.
- Ensure that your line passes through the origin and is straight.

### Quick Check:
- **Question 1:** If \( x = 4 \), what is \( y \) when the relationship is \( y = 5x \)?
- **Question 2:** True or False: The graph of the equation \( y = 0.5x \) is a proportional relationship.
- **Question 3:** What shape will the graph of a proportional relationship take on a Cartesian plane?

### Answers:
1. \( y = 20 \)
2. True
3. A straight line through the origin.

### Practice:
Try graphing the following relationships:
1. \( y = 2x \)
2. \( y = 0.75x \)
3. \( y = 4x \)

By practicing these steps, you'll improve your understanding and ability to graph proportional relationships effectively!