# Direct Proportion and Indirect 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 \( \frac{x}{y} = k \) [ k is a positive number], then x and y are said to vary directly. In such a case if \( y_1, y_2 \) are the values of y corresponding to the values \( x_1, x_2 \) of a respectively then \( \frac{x_1}{y_1} = \frac{x_2}{y_2} \).

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 \( y_1, y_2 \) are the values of y corresponding to the values of x respectively then \( x_1y_1 = x_2y_2 \) or \( \frac{x_1}{x_2} = \frac{y_2}{y_1} \).