Variation : If the value of one variable changes according to the changes in the value of some other variable,
then the relation between them is called variation.
Symbol `prop` is used to denote variation.
1. Direct Variation : If the ratio of the corresponding values of two variables is constant, they are said to be in direct variation.
It is denoted by `x prop y`
If `x prop y` then `x=ky` (constant `k!=0`).
2. Inverse Variation : If the product of the corresponding values of two variables is constant, they are said to be in inverse variation.
It is denoted by `x prop 1/y`
If `x prop 1/y` then `x=k/y` (constant `k!=0`).
3. Compound Variation : If a variable z varies as the product of two other variables x and y then z is said to be in compound variation with x and y.
It is denoted by `z prop xy`
If `z prop xy` then `z=kxy` (constant `k!=0`).
4. Partial Variation : If a variable y is divided into two parts such that one part a remains constant and the other part varies directly or inversely as x, then it is said that y varies partially as x.
`y=a+b`, where a is constant and `b prop x`, then `y=a+kx` (constant `k!=0`).
This material is intended as a summary. Use your textbook for detail explanation.
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