. Linear Function and its Real-Life Examples - Tech Trend Expert
Sunday, September 25

# Linear Function and its Real-Life Examples The word linear literally means arranged in a straight line. So a linear function can be defined as a function that represents a straight line. In a coordinate plane, a straight line is represented by the linear function. Let us take an example of a linear function to understand it more clearly. The equation y = 7x – 13 is a linear function because it represents a straight line on graph paper. In this article, we will discuss in detail the linear functions and their various concepts along with taking examples to understand the various concepts clearly.

### What Do You Mean by a Linear Function?

We can define a linear function as a function that represents a straight line on a coordinate plane. It is of the form y = f(x) = mx + b where m is a real number and b is a real number. In this equation, we have a dependent variable and an independent variable. We have y as the dependent and x as the independent variable. If you notice carefully, you will understand that this equation is similar to the slope-intercept form of a line. Let us take some examples of a linear to understand it more clearly.

• f(x) = y = 5x – 12
• f(x) = y = -6x – 7
• f(x) = y = 2x – 13
• f(x) = y = 13x – 1

### Some Real Life Examples of Linear Function

• A taxi service charges a fee of Rs 200 every month and an additional fee of Rs 10 per kilometer. Here, we can represent this scenario in the form of a linear equation y = 10x + 200 where y is the total cost and x represents total kilometers traveled.
• A web series streaming service charges a yearly fee of Rs 500 and an additional fee of Rs 50 for every web series that an individual watches. Here, we can represent this scenario in the form of a linear equation which is y = 50x + 500 where x is the total number of web series watched.
• We use the concept of linear functions in the chapter on linear programming problems. Linear programming problems are used to find optimal solutions.

### How Do We Find a Linear Function?

To find out a linear function, we use the point-slope form. To find out a linear function, we use the same steps as we do in the case of finding the equation of a line. Let us understand how to find out a linear function with the help of an example.

Example: Obtain the equation of a linear function that has two points (6, 10) and (8, 12).

Solution: It has given that (x1, y1) = (6, 10) and (x2, y2) = (8, 12).

Now, we will find out the slope of the function using the given formula:

Slope of the equation(m) = (y2 – y1) / (x2 – x1) = 12 – 10 / 8- 6 = 2 / 2 = 1.

Now, we put the values in the point slope form to obtain our required answer:

y – y1 = m (x – x1)

y – 10 = 1 (x – 6)

y = x + 4.

Thus, the required linear function is y = x + 4.

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