CBSE Class 8 Math, Direct and Inverse Proportions

•   If two quantities x and y vary (change) together in such a manner that the ratio of their corresponding values remains constant, then x and y are said to be in direct proportion.

•   if two quantities x and y vary (change) in such a manner that an increase in x causes a proportional decrease in y (and vice versa), then x and y are said to be inverse proportion.

•   If x and y are in a direct proportion, then

•   If x and y are in an inverse variation, then xy = constant.

The value of a variable is not constant and keeps on changing. There are many quantities whose value varies as per the circumstances. Some quantities have u relation with oilier quantities such that when one changes the other also changes. Such quantities are inter-redated. This is gilled a variation. Variation is of two types: (i) Direct variation and (ii) Inverse variation.

If two quantities are related in such a way that an increase in one quantity leads a corresponding increase in the other and vice versa, then this is a ease of direct variation. Also, a decrease in one quantity brings a corresponding decrease in the other.

Two quantities x and y are said to be in direct proportion, if

        

Note: I. In a direct proportion two quantities x and y vary with each other such that remains constant.

        II. is always a positive number.

        III. or k is called the constant of variation.