In mathematics, functions determine the type of relationship between two elements or variables. Therefore, they are very useful to describe phenomena, especially in areas such as Finance, Statistics, Engineering, Medicine, Economics, among others. Today we want to dedicate this article to talk about **what is a linear function and how is it represented**. So we invite you to read it if this topic is of interest to you.

To clarify your doubts, we have prepared this article. Stay with us and learn about what a linear function is.

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**What is a linear function and how is it represented?**

Within Analytic Geometry and Algebra, it is known as a first degree polynomial function that is represented as follows:

**f(X)*** = ***mX + b**

If we analyze the expression, we see how having the value of “X”, the first thing to do is multiply it by “m” and add the product to “b”. Therefore, the result of all this operation will be the value of f of “X” (f (X)).

Linear functions are very useful for calculating phenomena that occur in everyday life. For example, the cost of basic services such as water, electricity or gas, can be determined through this function. In addition to the amount, it will be possible to take into account the proportion in cases of increases.

Among the characteristics that can be mentioned of a linear function are:

- His representation in
**Cartesian plane**corresponds to a straight line (which is why it is known as a linear function). - “m” represents an exchange value, while “b” is a constant.

**Elements of the linear function**

Considering its form of expression f (X) = mX + b, the elements that make it up are:

- “X”:
**independent variable**(its value does not depend on any other variable and can be freely assigned). - f (X): in some cases it is represented with the symbol “y”. corresponds to the
**dependent variable**(its value depends on “X”). - “m”: refers to the
**earring**which determines the degree of inclination of the line. - “b”: is known as the origin and corresponds to the axis cut.

**Forms of representation of the linear function**

As we saw through an expression or formula it is used to represent a linear function, however, this process is also possible through a **table** or a graph.

To make it more clear **what is a linear function and how is it represented**Let’s go to an example.

**Table**

We have the following function: f (X) = 2X + 0

According to this formula it is possible to determine **which table** Y **values** they must register.

Here, the values of “X” were designated arbitrarily, while those of “y” originated from the calculation of a **Linear equation**:

y = mX

So, the first value is calculated from the multiplication of “m”= 2 by “X” = 0.

y = 2*0

= 0

While the second is calculated by “m” = 2 by “X” = 2. They are as follows:

*Y* = 2*2

= 4

When we look at the table and the operation we see how the **values represent** points that can be in the cartesian plane.

**Cartesian representation**

To the **graph** we take the values (*x and y*) embodied in the table, or those obtained through the operation and represent.

A = (0.0)

B = (2.4)

C = (4.8)

As we can see, a linear line with proportional growth is formed, which means that it is a **constant function **where the increase in value of “*x*”, is proportional to the value of “*Y*”.

Like every aspect of mathematics, linear functions are applicable in reality. For this reason, we invite you to train in what would be a specialized business school, where you can learn about this and other related topics.

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