Key Points - Direct and Inverse Proportions

- Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation.
- Direct Variation or Direct Proportion:
Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. That is if
 x / y = k [k is a positive number ], then x and y are said to vary directly. In such a case if  y1 , y2 are the values of y corresponding to the values x1, x of x respectively then
 x1 / y1   = 2 / y 2
- If the number of articles purchased increases, the total cost also increases.
- More than money deposited in a bank, more is the interest earned.
- Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.
- When two quantities x and y are in direct proportion (or vary directly), they are written as x ∝ y . Symbol ' ∝ ' stands for ‘is proportion to’.
- Inverse Proportion: Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if xy = k, then x and y are said to vary inversely. In this case if y1 , y2 are the values of y corresponding to the values x1 , x2 of x respectively then x1y1 = x2 y2 or -  x1 / x 2 = x 2 y2
When two quantities x and y are in inverse proportion (or vary inversely), they are written as x ∝ 1
. Example: If the number of workers increases, time taken to finish the job y
 decreases. Or If the speed will increase the time required to cover a given distance will decrease.