Overview
This lecture explains the concept of direct proportionality between two variables, shows how to represent it mathematically and graphically, and highlights key features of such relationships.
Direct Proportionality
- Two variables are directly proportional if as one increases, the other increases at the same rate.
- The proportional relationship is represented with a proportional symbol (∝) between two variables.
- For example, hours worked ∝ amount earned if pay rate is constant.
Mathematical & Graphical Representation
- If you double the hours worked, the amount earned also doubles; if you work 10 times as long, you earn 10 times as much.
- On a graph, a direct proportion is always shown as a straight line passing through the origin (0, 0).
- The axes are labeled with the two variables (e.g., hours worked and money earned).
- Example: 1 hour = £12, 2 hours = £24, 3.5 hours = £42, and so on.
Key Characteristics
- The graph for a directly proportional relationship is never curved, only a straight line.
- The line always passes through the origin (0, 0).
- Any pair of values on the line maintain the same multiplication factor (ratio remains constant).
Key Terms & Definitions
- Directly Proportional — When two variables increase or decrease at the same constant rate; if one doubles, the other doubles.
- Origin — The point (0, 0) on a graph where both variables are zero.
- Proportional Symbol (∝) — Notation indicating a direct relationship between variables.
Action Items / Next Steps
- Review example graphs of direct proportion.
- Practice plotting directly proportional relationships with different values.