Question

What is a variable? How do you distinguish a dependent variable from an independent one in a problem?

Short answer

Question: Define variable and explain the difference between dependent and independent variables in a problem. Answer: A variable is a symbol, usually represented by a letter, that can take on different values in a mathematical equation, function, or model. It is used to represent an unknown quantity or a changing quantity that depends on other variables. Dependent variables are variables whose values depend on the values of other variables in the problem, often representing the outcome or response. Independent variables, on the other hand, do not depend on the value of other variables in the problem and generally represent the factors that influence the dependent variables or cause the outcome. To distinguish between dependent and independent variables in a problem, identify which variables have values determined by other variables and look for the cause-and-effect relationship between them.

Step-by-step solution

Definition of a Variable

A variable is a symbol, usually represented by a letter, that can take on different values in a mathematical equation, function, or model. It is used to represent an unknown quantity or a changing quantity that depends on other variables.

Dependent Variables

A dependent variable is a variable whose value depends on the value of other variables in the problem. In a mathematical function or equation, it is the output variable, which means that its value is determined by the values of the input variables.

Independent Variables

An independent variable is a variable that does not depend on the value of other variables in the problem. In a function or equation, it is the input variable, which means that its value determines the value(s) of other dependent variables.

Distinguishing Dependent from Independent Variables in a Problem

In order to distinguish dependent variables from independent ones in a problem, it's important to identify which variables have values that are determined by the values of other variables and which ones do not. Look for the cause-and-effect relationship between the variables. Generally, the dependent variables represent the "effect" (the outcome or the response), and the independent variables represent the "cause" (the factors that influence the outcome).