## DIRECT AND INVERSE PROPORTIONS- ESSENTIAL POINTS

• 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, x2 of x respectively then x1/y1 = x2/y2.
• If the number of articles purchased increases, the total cost also increases.
• More than money deposited in a bank, more is the interest earned.
• Values that increase or decrease together are not always be in direct proportion, same in the case of inverse proportion.
• If quantities x and y are in direct proportion, they are written as x ∝ Symbol ' ∝ ' stands for ‘is proportion to’.
• Inverse Proportion: Two quantities x and y vary inversely if an increase in x results in a proportional decrease in y (and vice-versa) in such a manner that the product of their values remains constant. That is, if xy = k, then x and y are said to vary inversely. If y1, y2, are the values of y and values x1, x2 of x respectively then x1y1 = x2y2.
• If x and y are in inverse proportion, they are written as x ∝1/y. Example: If the number of workers increases, time taken to finish the job decreases.