Variation can be clearly understood if you know about Variables. In Mathematics, we generally deal with two types of quantities namely variables and constants. If the value of a quantity remains unchanged during different scenarios then it is said to be constant. On the other hand, if the value of a quantity changes under varying conditions then it is said to be a variable. Refer to the complete article to know about the Definition of Variation, Types of Variation, and Solved Examples on Variation, etc.
What is Variation?
In Mathematical Equations when a relationship is established there exist two types of quantities one is constant and the other is variable. Constant will not alter with the change in other parameters of the equation and the other is a variable that changes with different situations. The Changing of variable parameters is called a Variation.
You can understand the concept of variation with a simple equation y = mx
Here m is the constant and if we consider m = 2 then y becomes 2x
If x = 1, then y becomes y = 2*1 = 2
If x = 2, then y becomes y = 2*2 = 4
By changing the value of y, x gets different values. This is the variation of y with different values of x and similarly, you can get different values of y if the value of x changes.
Types of Variation
Variations can be of different types according to the pattern of changing or relationships of variables. We have explained the most common types of variation here and they are as follows
Direct Variation: If variables change proportionately i.e. either decrease or increase then it is said to be a direct variation. If A is in direct variation with B then it can be symbolically written as A α B.
Indirect Variation: In the case of Indirect or Inverse Variation variables change disproportionately i.e. when one variable increases the other one decreases. The behavior of Variables is exactly the opposite of direct variation. Thus, it is called an Indirect or Inverse Variation. If A is in indirect variation with B then it is symbolically written as A α \(\frac { 1 }{ B } \)
Joint Variation: If Two or more variables are related directly or one variable change with change product of two or more variables then it is said to be a Joint Variation. If A is in joint variation with B and C then it is symbolically represented as such A α BC
Combined Variation: Combined Variation is a combination of direct, indirect, or joint variation. In this kind of variation, three or more variables exist. If A is in combination with B, C then it can be symbolically represented as A α \(\frac { B }{ C } \) or A α \(\frac { C }{ B } \)
Partial Variation: If two variables are related using a formula or a variable is related by the sum of two or more variables then it is said to be a Partial Variation. y = mx+c is a straight line equation and is an example of Partial Variation.
FAQs on Variation
1. How do you define Variation?
Changing of Variable Parameters is called a Variation.
2. What are the Types of Variation?
There are different types of variation and they are as follows
- Direct Variation
- Indirect Variation
- Joint Variation
- Combined Variation
- Partial Variation
3. What is a direct variation proportion?
A Relations is said to be in direct variation when one variable changes and the second variable changes proportionally.