The duration of a trip is a variable dependent on the speed of travel.
In the field of mathematics , a symbol that is part of a proposition, an algorithm, a formula or a function and that can take on different values is called a variable . Depending on the way in which the variable appears in the function, it can be classified as dependent or independent .
The dependent variable is one whose value depends on the numerical value that the independent variable adopts in the function. One magnitude, in this way, is a function of another when the value of the first magnitude depends exclusively on the value evidenced by the second magnitude. 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 plans to take a car trip between London and Manchester . Both cities are 325 kilometers apart by road. The duration of the trip (which we can represent with the letter D ) will depend on the speed ( v ) of travel of the car. Duration, thus, is a variable dependent on speed, which is the independent variable.
If the journey is made at a constant speed of 120 kilometers per hour , the journey time between London and Manchester will be just over 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 ).
When fruits or vegetables are purchased by weight, the price to pay is a variable dependent on the quantity purchased.
The price, a common variable dependent on the weight
The money 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 two kilograms are purchased or 40 pesos if four kilograms are purchased. The amount to pay, in this way, is a variable dependent on the number of apples purchased.
In the field of geometry , where the creation of graphs to appreciate the results of an endless number of mathematical functions is very common, the aforementioned duality of dependent and independent variables always appears, generally under the name of y , x and 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 the Greek.
The importance of context
A very important aspect to highlight about this concept is that no variable is always dependent or independent , but rather this depends on the context in which they are used; In other words, dependence or independence is not an inherent property of any variable. To understand this particularity, we can return to any of the examples presented above and modify them slightly.
On the trip from London to Manchester, given that the road had already been previously chosen at the time of presenting the statement, distance seems to be an independent variable, and the same is true of speed. However, always on a theoretical level, what would happen if the driver wanted to travel at a particular speed, regardless of the path he chose? What if you intended the trip to last a fixed amount of time, and this affected the speed and distance? As can be seen, the variables are like pieces in a board game, and scientists can move them as they wish.
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 would be the independent variables, while the results in the subject would be the dependent variables.