Is Dependent X Or Y

Mentor: Today we are going to discuss independent and dependent variables. What does it mean for something to exist independent?

Educatee: That means that it doesn't depend on anything else.

Mentor: That's right! And so what practice you think it means for a variable to be independent?

Pupil: Maybe that variable doesn't depend on the other variables or numbers.

Mentor: Right. In mathematical terms, we call a variable contained if its value can be gear up arbitrarily to go a event. This is known as the input of a function. Do you know what I mean past "input"?

Pupil: That'southward the variable that you offset with. Y'all know that variable, so you exercise something to it, and y'all get the "output".

Mentor: Correct, and we correspond the variables with x and y. When you input a value of 10 into an equation, y'all get a value for y. And so if 10 is the independent variable, what identity does y have?

Educatee: Since y is the output of the function, I guess y would be the dependent variable. Its value is dependent on whatever the value of ten is.

Mentor: That'due south correct, y is the dependent variable because we practice not prepare a value of y directly; instead, we gear up a value of x and employ that to find the value of y. Consider this simple equation as an example:

Mentor: In this equation, what are the independent and dependent variables?

Student: Well, for whatsoever value of ten, you have to multiply it by two and so add together i to get y, so y is dependent on x. The independent variable is ten, and the dependent variable is y.

Mentor: Indeed. Information technology is relatively piece of cake to place the contained and dependent variables in a simple two-variable equation, simply what practice you make of this equation:

Student: Yikes! I don't know what to do with more than than two variables. I approximate y would nonetheless exist the dependent variable, but I don't know which of x and z is the contained variable.

Mentor: You're right on both counts. x and z are both independent variables. You can change either variable to whatever value before determining the value of y.

Student: Okay, I think I've got information technology. The variable that's lone is the dependent variable, all other variables are independent.

Mentor: That'southward right, but what if I change the equation around a bit? What happens when I solve the equation for z:

Student: Then... z is the dependent variable, and x and y are independent. But I thought you said that y was the dependent variable.

Mentor: I did say that, but the independent and dependent variables are not and so immutable as they might seem from an algebraic perspective. With any equation, you tin can arbitrarily set any variable as the dependent variable, and then gear up all others every bit independent variables. In fact, what you've learned about dependent and contained variables has very petty to do with pure algebra.

Student: And so why bother? Why not just randomly option out variables to be independent and dependent?

Mentor: Consider the idea of driving a motorcar. The acceleration of the car changes based on the pressure you put on the accelerator and the restriction, approximated by the equation:

Mentor: Where a is the acceleration, p is the pressure on the accelerator, and b is the pressure on the brake. In this equation, what is the dependent variable?

Student: Acceleration, a is dependent.

Mentor: Right, but fifty-fifty if I rearranged the equation to read:

Mentor: It wouldn't make any sense to say that the force per unit area you put on the brake depends on your acceleration. Conspicuously, it is acceleration that depends on braking, not the other way around. And pressure on the brake certainly doesn't depend on pressure on the accelerator.

Student: So I guess when you are talking about existent-world phenomena, the idea of independent and dependent variables becomes more than important.

Mentor: Exactly. Especially when you outset learning to perform scientific experiments, the thought of independent and dependent variables volition exist important conceptually, fifty-fifty if information technology is not of import algebraically.

Is Dependent X Or Y,

Source: http://www.shodor.org/interactivate/discussions/IndependentDependentVariables/

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