#### notes

For example : find the cost of 5 kg or 8 kg of sugar. Study the following table.

Observe that as weight of sugar increases, cost also increases in such a manner that their ratio remains constant.

We say that x and y are in direct proportion, if `x / y = k `"or"` x = ky.`

If x and y are in direct proportion, we can write `x_1 / y_1 = x_2/y_2`

`[y_1,y_2` are values of y corresponding to the values `x_1,x_2` of x respectively]

Thus, variables increasing (or decreasing) together need not always be in direct proportion. For example:

(i) physical changes in human beings occur with time but not necessarily in a predetermined ratio.

(ii) changes in weight and height among individuals are not in any known proportion and

(iii) there is no direct relationship or ratio between the height of a tree and the number of leaves growing on its branches.

#### Shaalaa.com | Introdution

#### Related QuestionsVIEW ALL [40]

Complite the following table given that *x* varies directly as *y *.

x |
2.5 | ... | ... | 15 |

y |
5 | 8 | 12 | ... |