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Concept of Direct Proportion

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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.

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