1. Definition and judgment: Proportional relationship: When the ratio of two quantities is constant, that is, the multiple of one quantity's increase is equal to the multiple of the other quantity's increase, then these two quantities are said to have a proportional relationship. Inverse proportionality relationship: When the product of two quantities is constant, that is, when one quantity increases and the other quantity decreases accordingly, and their product remains unchanged, then these two quantities are called inverse proportionality.
2. Graphic representation: Proportional relationship: In a Cartesian coordinate system, if the relationship between two variables is represented by a straight line passing through the origin, then they are in a proportional relationship. Inverse proportional relationship: In a Cartesian coordinate system, if the relationship graph between two variables is hyperbolic, then they form an inverse proportional relationship.
3. Practical application example: Proportional relationship: For example, when the speed is constant, the distance and time are directly proportional because the distance=speed x time. If the speed remains constant, the distance increases with time, and the increase is the same multiple. Inverse proportionality relationship: For example, under a constant total workload, work efficiency is inversely proportional to work time, because the higher the work efficiency, the less work time is required, and their product remains constant.