Inverse Proportion

Inverse proportion occurs when one quantity increases while the other decreases. If you double one, the other is halved.

The Mathematical Formula

The relationship is expressed as: $$y = \frac{k}{x} \quad \text{or} \quad xy = k$$

Key Characteristics

1. The product $x \times y$ is always constant ($k$).
2. The graph is a curve (hyperbola) that never touches the axes.

Example: Speed and Time

If it takes 4 hours to travel a distance at 60 mph, how long will it take at 80 mph?

1. Find $k$: $60 \times 4 = 240$ (The total distance).
2. Apply to new value: $t = \frac{240}{80} = 3$. Answer: 3 hours.