This article is a continuation from Part I, which discusses about direct proportion.

**Inverse Proportion**

Two sets of readings for the quantities *x* and *y* are given in the table below.

| 3 | 4 | 6 | 12 |

| 4 | 3 | 2 | 1 |

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 (x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}), …, we can say

xy = x_{1}y_{1} = x_{2}y_{2} = x_{3}y_{3} … = k

**Notes:**

- When a variable is proportional to two or more variables, we can represent this relationship as a
**joint variation**. For example,

When*y*∝*x*and*y*∝ z

therefore*y*∝*xz*or y =*kxz*

When

therefore

- In every proportional relationship, the converse is also true. For example,

Ify∝x, thenx∝ y.

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…

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