Question

On increasing$a,b$ increases in such a manner that$\frac{a}{b}$ remains ______ and positive, then$\text{a and b}$ are said to vary directly with each other

Answer 1

Direct Proportion: If two quantities$\text{x and y}$ vary directly with each other, then ratio of their corresponding values remains constant.

Two quantities $\text{a and b}$ are said to be in direct proportion if they increase or decrease together. In other words, the ratio of their corresponding values remains constant. This means that,

$\frac{a}{b}=k$

where. $k$ is a positive number, then the quantities $\text{a and b}$ are said to vary directly.

In such a case if the values ${\text{b}}_1,b_{2}ofb$ corresponding to the values $a_1,a_{2}ofa$ respectively then it becomes;

$\frac{a_1}{b_1}=\frac{a_2}{b_2}$

The direct proportion is also known as direct variation.