In the field of **math**, is named **variable** to a symbol that is part of a proposition, an algorithm, a formula or a function and that can **adopt different values**. According to the way in which the variable appears in the function, it can be qualified as **dependent** or **Independent**.

The **dependent variable** is the one whose **value** depends on the numerical value that the **independent variable** in function. In this way, one quantity is a function of another when the value of the first quantity depends exclusively on the value shown by the second quantity. The first magnitude is the dependent variable; the second magnitude, the independent variable.

## The example of the duration of a trip and the speed

Suppose a **person** plan to take a car trip between **London** Y **Manchester**. Both cities are located **325 kilometers away** by highway. The duration of the trip (which we can represent with the letter **D**) will depend on the speed (**v**) of the car’s displacement. Duration, thus, is a variable dependent on speed, which is the independent variable.

If the trip is made at a constant speed of **120 kilometers per hour**, the duration of the trip between **London** Y **Manchester** will be little more than **2 hours and 42 minutes**. On the other hand, if the vehicle travels at **80 kilometers per hour**, the duration of the trip will be extended to **more than 3 hours**. As can be seen, the magnitude **D** is a variable dependent on the magnitude **v** (the **speed**).

## Price, a common weight-dependent variable

The **money** What is paid to buy apples, on the other hand, depends on the quantity chosen. If the price per kilogram of apples is **10 pesos**, the total to pay will be **20 pesos** if they are bought **two kilograms** or **40 pesos** if they are acquired **four kilograms**. The amount to be paid, in this way, is a dependent variable on the number of apples that are bought.

In the field of **geometry**, where the development of graphs is very common to appreciate the results of an endless number of mathematical functions, the aforementioned duality of dependent and independent variables always appears, usually under the name of **Y**, **x** Y **z**, since they are the letters associated with the Cartesian axes, although there are many used in traditional formulas, and they are taken from both our alphabet and Greek.

## The importance of context

A very important aspect of this concept to highlight is that **no variable is always dependent or independent**This depends on the context in which they are used; In other words, dependency or independence is not a **property** inherent in no variable. To understand this particularity, we can take any of the examples set out above and modify them slightly.

On the trip from London to Manchester, since the road had already been chosen previously at the time of presenting the statement, the distance seems to be an independent variable, and the same happens with the speed. However, always on the theoretical level, what if the driver wanted to travel at a particular speed, regardless of the path he chose? What if you wanted the trip to last a fixed amount of time, and this affected speed and distance? As can be seen, the variables are as **parts** of a board game, and scientists can move them as they please.

It is worth mentioning that the concept of the dependent variable and its inevitable counterpart, the independent variable, also appear outside the scope of mathematics and physics; for example, medicine and psychology can take advantage of them **to measure the consequences of a treatment on a patient**. In a case like this, the characteristics and properties of the **treatment** They would be the independent variables, while the results in the subject, the dependent ones.

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