Difference Between Linear and Non-Linear Equations For Easy Understanding

Difference Between Linear and Non-Linear Equations For Easy Understanding

Mathematics is full of equations and functions, and while it can be overwhelming, one requires the basics of maths in everyday life. Some equations come with numbers, some come with variables, while a few would consist of both. 

Equations are mostly used to express the equality of two algebraic expressions. However, what we are here to learn about would be linear and nonlinear equations. Before learning about the differences, it is crucial to learn what linear and non-linear equations are. 

Professionals alongside mathematicians use equations in everyday life for statistical procedures gaining different results. You would come across several equations in your lifetime; especially, if you take up mathematics for your higher studies. 

Here is everything you need to know about the difference between linear & nonlinear functions

What Defines An Equation? 

An equation can be defined as a statement where the mathematical value of the two expressions would be equal. Professionals and mathematicians often use equations in various algebraic and statistical processes to figure out the known value. 

It is possible to replace the equation values with similar variables that help you or represent the possible accurate solutions. Equations are of many use, including graphing them, determining values or even patterns. 

What Is A Linear Equation? 

A linear equation forms a straight line as linear is related to a straight line. Linear equations are conditions of the principal request and are widely used to construct a straight line. Lines define the equation conditions within an arranged framework. 

When constructing a straight line, linear equations are used routinely. They appear in powers of one, and the overall portrayal of the linear equation would be y=mx+b, where m is the slant and b would be the y-catch. 

Solve the linear equation 3x+9 = 2x + 18.
Given, 3x+9 = 2x + 18
⇒ 3x – 2x = 18 – 9
⇒ x = 9

Examples Of Linear Equation 

For Finding Variable Costs 

Linear equations can be used for finding variable costs. An example would be — if you are employing a painting contractor for Rs. 500 a day, and Rs.50 for each square foot, then you could determine using linear equations how much you have to pay the contractor. In the equation, y would be the square foot that requires painting; therefore, 

x= 50y+ 500

To Determine Rate Calculation 

For any kind of work, it is crucial to get the rates compared, and for that, you could easily use a linear equation. If you wish to hire a catering service, the first company might charge you Rs.10,000 for the whole day while the second one might charge you Rs.1000 per hour. 

If you know how many hours the event would last (let’s say 5 hours), linear equations will help you determine which one would be more profitable for you. 

How to determine the cost of the first catering company? 

10,000= 5x

How to determine the cost of the second company? 

y= 1000(5)

Determining Earnings 

This would help you determine how much you might earn using a linear equation. For example: if you are in a band and you see an event is paying you Rs. 5,000 for the performance and Rs. 100 for every ticket sold, then you could determine what your earning would be on that day. y determines the earning, and x represents the tickets one could sell. 

y= 100x 5000

What Is A Nonlinear Equation? 

When you graph a line, and it becomes a curved line, then the equation is termed a nonlinear equation. When using unknown variables, if the output of the equation is found to be inconsistent, then it can be termed as a nonlinear equation. 

Nonlinear equations could be simple curves or even elaborate images. They do not appear in powers of one. 

Examples

  • x2+y2 = 1
  • x2 + 12xy + y2 = 0
  • x2+x+2 = 25

Examples Of Non-Linear Equations 

Regression Analysis 

This is a popular statistical technique that often professionals opt for to study variables of interest. Regression analysis could be used with both linear and nonlinear equations. You can even opt for it for making predictions alongside estimating effects. 

Here is a nonlinear equation for regression analysis 

y1= a+bx

Logarithmic Scales 

To show exponential growth on a graph, a logarithmic scale nonlinear equation is used. This is applied in several fields, including medicine, mathematics, actuarial science, forensic science, archaeology, geology, and finance. 

Examples of logarithmic scales would be the pH scale, the Richter scale, and also decibel systems.

y=log10(x)

Using S-curve Graphs  

S-curve graphs are often used in project management to track the progress and determine the scope of the particular project. Several nonlinear equations could be used to produce an S-curve graph, but here is a simple one:

y=3x^2 -2x^3 

What Are The Major Differences Between Linear And NonLinear Equations? 

  • When it comes to studying and analysing subjects like physics and mathematics, often researchers and professionals consider linear equations to be the simpler ones and nonlinear equations alongside graphs to be a bit more complicated. 
  • A linear equation is always represented using a straight line, while nonlinear equations could be simple curves and other non-straight lines. It could be an S-curve or could even be a bell-shaped graph. 
  • When putting different variables into a linear equation, the output you get would be similar every time; however, with nonlinear equations, when putting unknown variables, the difference in output would be noticed every time.
  • A linear equation comes with a maximum of one degree, while a nonlinear could be two or even more. A nonlinear equation would never have less than two degrees. 

Conclusion 

As discussed, linear equations are best for explaining linear relationships. For example, through a linear equation, it would be easy to discuss how the number of cookies could directly impact your weight. 

Therefore, this is everything to help you understand linear and nonlinear equations and their major differences. 

Now that we have covered linear and nonlinear equations in detail, we hope you can solve equations without any hesitation. Make sure to revise the concepts regularly so you can keep up with the equations and their calculations. 

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