6.3 Variation

It is the relation between a set of values of one variable and a set of values of other variables.

Direct Variation: If variables x and y are such that for any corresponding values of these variables, we have the value of y/x as constant, we say that y varies directly as x or y is proportional to x or the variation in y is the same as the variation in x. In symbols, this is expressed as same as the variation in x. i.e. y µ x

If the constant value of y/x is denoted by k then k is called constant of proportionality or constant of the variation.

So, when y µ x, we have y = kx for some k and when for some k, y = kx, we have y µ x.

Example If x µ y and x = 15 when y = 5 find :

i) y when x = 9 ii) x when y = 8

When x = 15, y = 5

        = 3

       = k

Now i) Substitute x = 9 in x = 3y

\ 9 = 3y \ y = 3

ii) Substitute y = 8 in x = 3y

\ x = 3 ´ 8 = 24