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
Solution : x µ y . Therefore,
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
