This article is a continuation from Part I, which discusses about direct proportion.
Two sets of readings for the quantities x and y are given in the table below.
Here, when x is doubled, y is halved; when x is trebled, y is one-third its previous value and so on.
We say that y is inversely proportional to x, or y varies inversely as x, that is
The graph of y versus x is as shown:
Notice that the product of x and y is the same for every point (12 in this case). Hence this product is known as the constant of proportionality or variation and it is given a symbol such as k. Therefore, we can write the exact relationship between x and y as
Assuming that there are points (x1, y1), (x2, y2), (x3, y3), …, we can say
xy = x1y1 = x2y2 = x3y3 … = k
Examples of physical quantities that vary inversely with each other are:
- Pressure and volume
- Frequency and periodic time
- Gravitational force and the distance squared
To be continued…