Direct and inverse proportion refer to the relation between two variables thatdefines how the value of one variable changes when the value of the other variable is changed. ... On the other hand if y is inversely proportional to x, when x increases y decreases and when x decreases y increases..

Direct Proportion
In direct proportion, two quantities increase or decrease together. When one quantity increases, the other also increases at a consistent rate, and when one decreases, the other follows suit. This relationship can be expressed mathematically as:
- If \( y \) is directly proportional to \( x \), then \( y = kx \), where \( k \) is a constant.
Key characteristics of direct proportion include:
- Constant Ratio: The ratio of the two quantities remains constant.
- Graphical Representation: The graph of two directly proportional quantities is a straight line passing through the origin.
- Example: If you buy more items at a fixed price, the total cost increases directly with the number of items.
Inverse Proportion
In inverse proportion, one quantity increases while the other decreases. Their product remains constant, meaning that as one quantity becomes larger, the other becomes smaller. The mathematical representation of this relationship is:
- If \( y \) is inversely proportional to \( x \), then \( y = \frac{k}{x} \), where \( k \) is a constant.
Key characteristics of inverse proportion include:
- Constant Product: The product of the two quantities remains constant.
- Graphical Representation: The graph of two inversely proportional quantities forms a hyperbola.
- Example: If you drive faster, the time taken to reach a destination decreases, illustrating inverse proportion.
Understanding these two types of proportional relationships is crucial in various fields, including mathematics, physics, and economics, as they help in predicting and analyzing real-world situations effectively.