Question

How do you know if an equation is linear or nonlinear?

Answer 1

Hint: A linear equation is used to represent a straight line in a graph, whereas non-linear equations are used to represent curves.

Complete step by step answer:
An equation is considered linear if it is in the form of $y = mx + b$ where m is the slope of the equation and b is the y-intercept.
Notice how here, x can only be to the power of one. In here, the conditions are just simply $m,b \in \mathbb{R}$.
Some examples include $y = 5x + 4,y = x - 2,y = 0,$ and even some like $x = 1$.
As you can see here, all of the following equations are represented using a straight line.
An equation is considered “non-linear” when it is not graphed using straight lines. Some examples include $y = 3{x^2} + 1,y = 2{x^3} - 3,y = {x^5} + 43$.
In conclusion, a linear equation will always be in the form of $y = mx + b$, where m is the slope of the equation, and b is the y-intercept of the equation.

Note: To determine if an equation is a linear function, it must have the form $y = mx + b$ (in which m is the slope and b is the y-intercept). A nonlinear function will not match this form.
In a linear equation, the variables appear in first degree only and terms containing products of variables are absent. But in the case of nonlinear equations, at least one variable is not of the first degree or the equation contains a product of variables.
An equation is linear if its graph forms a straight line. This will happen when the highest power of x is $1$. Graphically, if the equation gives you a straight line then it is a linear equation. Else if it gives you a circle, or parabola, or any other conic for that matter it is a quadratic or nonlinear equation.
If the highest power of x in the equation is one then it is a linear equation else if the power of x is greater than one then it is nonlinear.