Mathematics is a vast subject with definite applications in daily life scenarios. It is linked with all sorts of small and big businesses. It is very important to know the basics of Mathematics. Even in our academic curriculum, the most important subject which is an integral part of different fields is Mathematics. This subject is very interesting if one pays attention to it and practices all kinds of problems otherwise it can be a nightmare. A function is the basic component of Mathematics. It is generally a relation which links two different members of different sets. It can also be defined as a relation between two variables. A function is of many types but the most important among them is a linear function. This function has a huge range of applications both in basic and higher mathematics. A linear function is one whose graph resembles a straight line. It comprises an independent variable and a dependent variable. The definition of a linear function has been explained very well on Cuemath, an online maths and coding platform for young minds. This platform makes learning very creative. Here, we will be discussing in detail all the important terminologies related to a linear function.
Fundamentals of a linear function:
- Definition: A Linear function is a specific function in algebra in which the terms involved are either constant or product of any constant and an individual variable.
- Graph: The graph of a linear function resembles a straight line and is accompanied by a slope.
- Representation: They are represented as equations and are identified by their respective slope and the y-intercept formed.
- Different lines: The linear function can represent two different lines horizontal or vertical. Vertical lines have an unknown slope whereas horizontal lines have a slope whose value is zero.
- Slope: This factor determines the gradient or inclination of any line. This is the most important aspect of a linear function. This part helps in solving an equationor creating an equation. If one can easily determine the slope of a line then it is very easy to understand the concept of a linear function. This also indicates the direction of a line which facilitates us in identifying whether it is an increasing line or a decreasing line. Slope can be evaluated by dividing the vertical alteration by the horizontal alteration.
- Variation: Two variables can share either a direct variation or an inverse variation. If they are in direct variation then any alteration in one leads to a similar alteration in the other. In the case of inverse variation, any alteration in one variable results in a similar change in another variable but just in the opposite direction. Variation plays a vital role in solving complex problems on a linear function.
- Application: Linear function can easily solve problems in daily life. Once a graph is formed and we determine the equation and the values given to us are represented carefully on the graph we can easily apply the principles of a linear function to solve any sort of complex problem. This clearly defines the significance of linear function in real life. Many companies imply the concept of a linear function to solve their complex problems. The linear function also finds its use in calculus and higher mathematics.
- Forms: Linear function is of two different forms- the slope-intercept form and the point-intercept form. It is very important to know the process of interconversion between these two forms.
The linear function is that portion of mathematics that is useful for both middle-class students and students of higher classes. Therefore, it is very important to clear the concepts of the linear function. Questions on linear functions are asked in critical examinations. Mathematics can be mastered only through practice. Problems and concepts of linear function require a lot of practice for any student to develop clarity. Linear function questions may appear tricky but once one understands the fundamentals well and picks up the pace, it will be very easy to master them. Here, we have discussed all the important concepts related to the linear function. We hope that it was helpful.
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