Question

What are linear and non-linear?

Answer 1

Hint: We will find the different equations as examples that are formed from the two variables x and y. We will then determine the exponent or power of those variables to identify and explain the linear and non-linear.

Complete step-by-step solution:
There are two different types of equations in algebra: linear and nonlinear equations. Equations are categorized as linear or nonlinear based on the exponents of variables. Non-linear equations have the greatest exponent of 2 or more but not less than 2, whereas linear equations have the highest exponent of 1.

Case 1: Let’s discuss a few points about the linear equations.
1) The formula for any linear equation is y = mx + C.
2) Linear equations have a constant slope and are graphed as a straight line.
3) 2x + 3 = 0, x = 2 and z = 2z – 1 are the few examples of linear equations. Each equation has a maximum degree of one.

Case 2: Now, we will discuss a few points about the non-linear equations, which are exactly the opposite of the linear equations.
1) Any equation whose degree is greater than one is a non-linear equation.
2) The slope of non-linear equations always varies at different points and so they are not straight lines but a curve.
3) Equations of the circle, ellipse, parabola, and hyperbola are a few examples of non-linear equations. Each of them forms a curve.

So, non-linear equations have the greatest exponent of 2 or more but not less than 2, whereas linear equations have the exponent of variables as 1 .

Note: Just by looking at the equations we cannot tell whether it is a linear equation or a non-linear equation, but we can always tell by looking at the graphs of the equation. For example, the specific equations of logarithm or trigonometric functions are linear but others are non-linear.