As the name indicates, a variable is something that is changing under some circumstances or varies without restraint.
Math uses different graphemes such x,y,z,alpha,beta.. to designate a variable.
Seeing the equation f(x) = mx + b, you easily may recognize a linear function, just looking at the power of variable x. You may use instead of the map f(x), the letter y = f(x). This letter y denotes a variable that is changing with respect to x, which is involved in the relation mx+b.
If you look at the action, a constant may be defined as the opposite of a variable(if you wish, a constant denotes the antonym of a variable), hence the value of a constant stays the same and it is not changing under any circumstances.
THEY ARE BOTH A WAY TO DESIGNATE NUMBERS
now a number may stand for value,magnitude etc, of something
now when we know the exact value, magnitude etc, we give it it's specific value this value ;if not subject to any change i,e. is non variable is called a constant
but often we dont know the exact value, in such cases we denote this value by some"symbol"(eg,X) but realise that this symbol is subject to change (eg Y,Z ETC)THIS SYMBOL IS THEREFORE CALLED "VARIABLE" ie some thing that can change
In maths, you will encounter many "letters". This "letters" are the symbols used to form equations and mathematical expressions. ("letters" here may mean symbols like the theta, beta, etc) Some of these symbols are constants and some represent variables. Knowing what are constants and variables is crucial for mastery of maths learning. What are constants? Constants, as the word literally means, are items that have number that never change. What are variables? Variables are symbols that changes in value. Example A: y = 3 x + 2 y and x are variables, and 3 and 2 are obviously constants. Example B: log x = 5y x and y are variables , and 5 is constant. Example C: y = mx + c ( for straight line equation) y and x are variables, and m and c are constants. This may be confusing to some maths students when they start plotting graphs. Here, the straight line is continuously moving with the value of x and y. So why is the "m" identified as constant? You need to know that "m" represents the "GRADIENT" of the line. The line has the same slope at any value of x and y. Thus "m" is a constant. This is a typical concept that commonly goes wrong. Therefore when you really understand what changes are considered "variables" and those that remain stable are known as "constants", you are in line for good maths study!