Online Class #23 ll ভেদ দশম শ্রেনীর ll variation Class x Math l Part 1 ll

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Variable and Constant:
In Mathematics, we usually deal with two types of quantities-Variable quantities (or variables) and Constant quantities (or constants). If the value of a quantity remains unaltered under different situations, it is called a constant. On the contrary, if the value of a quantity changes under different situations, it is called a variable.
For example: 4, 2.718, 22/7 etc. are constants while speed of a train, demand of a commodity, population of a town etc. are variables.

In a mathematical equation where a relationship is established for some type of parameters normally two types quantities exist. One is constant that doesn’t change with the changes of other parameters in the equation and another is the variables which change for different situations. The changing of variable parameters is called as variation.

In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value ( or values ) of the related variable (or variables). Suppose a train running at a uniform speed of v km./h. travels a distance of d km. in t hours. Obviously, if t remains unchanged then v increases or decreases according as d increases or decreases. But if d remains unchanged, then v decreases or increases according as t increases or decreases. This shows that the change in the value of a variable may be accompanied differently with the change in the values of related variables. Such relationship with regards to the change in the value of a variable when the values of the related variables change, is termed as variation.

This can be explained by an example of simple equation y = mx where m is a constant. If we assume that the value of m as 5 then the equation becomes as y = 5x.

When x = 1, y = 1 × 5 = 5

When x = 2, y = 2 × 5 = 10

When x = 3, y = 3 × 5 = 15

Simply the value of y is changing with the different values of x.

This is the variation of y with different values of x and similarly it can be shown that with different values of y the value of x changes.

Variation can be of different types according the pattern of changing or relationships of variables.

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