A linear function can be defined as a function where each term used is a constant or a product of the same constant and is a single variable. Let us take an easy example of this. The equation, y = mx + b, is linear since it meets all the requirements utilizing x and y as variables and m and b as constants. This equation is linear since the power of x is related to one and it follows the definition of a function which states that for every input x, there is exactly an output y. Eventually, when it is placed on a graph, it represents a straight line.
Graphically representing a linear function
The word ‘linear’ comes from the concept that it would form a straight line for the solution of a set of equations. When jotting down on a graph, a linear function is represented using the constant m which is the slope or gradient and the constant b is the point where the line touches the y-axis or commonly known as the y-intercept.
Real-life scenarios utilizing linear function
There are a few real-life scenarios in which linear function is used by utilizing the formula y =mx + b.
- We can find the amount of electricity consumed for the nth day. For instance, an average amount of electricity is consumed per day. Say it is 20 units. So to find out the amount of electricity consumed at the end of the nth day can be written as: y = 20 * n + 0. Here y is the amount of electricity consumed for a total of n days.
- Another example of a linear function can be demonstrated by taking a car for rental purposes. Let us assume that the rental charges for the car are $20 and an extra $7 is levied for every hour. Thus we can write a linear function over this example. The function would look like this: y = 7 * t + 20, where ‘t’ is the total number of hours.
- We can also use a different example to find out a linear function. For example, there is a car travelling at the speed of 85 miles per hour. So, after n hours, how much distance is traversed by the car? This we can put it into an equation and it looks like: y = 85 * n
- Linear equations can be used to ascertain an employee’s cost to the company. For instance, a company pays $500 and another company pays $12 per hour. Both the companies insist on working for a total of 40 hours per week. We have to find out which company offers the best wage. This is where the concept of a linear equation comes into play. The first equation can be expressed using the formula, y = mx + b. Thus, we can write 500 = 40x which is the offer proposed by the first company. Thus the result comes to $12.5 per hour. Similarly, for the second company’s offer, we can write it as y = 12 (40) which is equal to 480. Therefore, the pay rate of the first company is much more than the pay rate proposed by the second company.
Linear equations are nowadays used extensively in solving complex problems. With the help of the formula, it becomes easier to solve the equation and later utilize it for mathematical purposes. Cuemath has been helping students with these concepts and is emerging as a giant in conducting online classes on mathematics. For getting a better view of the concepts, you can visit Cuemath website.