What Are Linear Functions?
In mathematics, functions can be defined as the relation from a group of inputs that are used to get a suitable output where the nature of inputs is similar to that of outputs. There are various functions such as exponential function, non-linear function, and so on. Likewise, a linear function is a type of function that expresses or represents a horizontal and a vertical line on a coordinate plane. For example, x = 3y – 2 which represents a straight line on the plane, and thus it expresses the linear function. The formula given for the linear function is, y = mx + b. Here, ‘m’ is defined as the real number along with ‘b’ whereas ‘x’ is regarded as the variable which is independent in nature. In this article, we will try to cover some basic concepts regarding linear function such as comparison between linear and nonlinear functions, real-life examples of it, and do a detailed analysis about them.
Comparison Between Linear and Nonlinear Functions
In the paragraph mentioned above, we dealt with the basic concepts regarding linear functions along with their definition. In this passage, we will try to cover the comparison between linear and nonlinear functions. The following points mentioned below analyze the distinctive features between them;
- A type of function which represents a straight line that consists of degree 1 is defined as the linear function whereas a type of function which does not express a straight line and consists of degrees more than 1 can be defined as a nonlinear function.
- When a linear equation is plotted on a bar or a coordinate graph, it forms a straight line whereas a nonlinear equation forms a curve, when plotted on any graph.
- A general equation formed by a linear equation is y = mx + b, where ‘b’ and ‘m’ signify the real numbers and ‘x’ as an independent variable. A general equation formed by a nonlinear equation is ax.ax + by.by = c. Here, ‘a’, ‘c’ and ‘b’ are signifying constant values whereas ‘y’ and ‘x’ represent variables.
- Some examples of linear function are as follows, 4x + 3 = 5, 3x + 2 = 5, some examples of nonlinear function are as follows, 3x.3x – 5x + 1 = 0 etc.
The points mentioned above will help you to distinguish between a linear and nonlinear function if portrayed in any type of graph.
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Some Real-Life Examples of a Linear Function
Till now, you may have understood about linear function, if yes, then let us look into the real-life situations or examples of linear functions. Some of the examples are as follows.
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- Let us assume that a streaming website of movies and web series charges a monthly subscription of, rupees 4.50 and a charge added for downloading the content of rupee 0.35. Thus, the total charge of the subscription for the streaming website can be represented in the form of a linear function as, 4.50 + 0.35x. Here, x is the total number of movies that are being downloaded.
- Assume that a sporting company charges a price of rupees 50 and 8 per shoe to be signed by famous personalities. Thus, the total charge represented in the form of a linear equation is 8x + 50 where ‘x’ is the price per shoe to be signed.To find more information about importance touch here Mywikinews
Visit Cuemath Website to Master Math
More often than not, mathematics as a subject becomes boring and creates an environment where you do not understand anything about it. But to master math, conceptual clarity is very important and that is when the job of Cuemath comes into work. If you want to learn about various topics such as linear functions and many others which require physical assistance and conceptual clarity, you may visit Cuemath’s website and master math.
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