What is independent variable in an example?

Answer 1

Assume you have a function:

y = mx+b

assume m and b are constants (i.e., they don't change)

y and x are variables.

y is a function of x, and the function can be rewritten as:

f(x) = mx+b

Because y is a function of x, that means y depends on x. In other words, when x changes, y changes.

But x is not dependent on y. It can be whatever it wants to be. So x is an independent variable.

The simple way, that usually works, is to remember the variable that is by itself is probably dependent, while the variable that is not by itself is probably independent (I know this sounds a little backwards).

In the example:

y = mx + b
y is all by itself on the left side, so it's dependent
x is hanging with m and b, so it's independent

A real world example:

s(t) = 2t + 5t2

with s as Speed and t as Time.

You can look at that and see, that depending on what time you plug into this equation, the speed will change.

s(1) = 2(1) + 5(1)2 = 2 + 5 = 7
s(2) = 2(2) + 5(2)2 = 4 + 20 = 24

Therefore s (speed) is the dependent variable (it's all by itself on the left side)
and t is theindependentvariable (it's hanging out with some other numbers)