What are Linear Equations?

Linear equations are nothing but another set of equations. Any linear calculations or solving requiring more than one variable can be done with the assistance of linear equations. The standard form of any linear equation in which one variable is in the form ay + b = 0. Here, y is a variable, and a and b are the constants. Although, the standard form of any linear equation in two variables is of the form ay + bx = c. Here, y and x are variables, and a, b, and c are the constants. 

In simple words,

Linear equations are equations of the first order. These linear equations are defined for the lines in the coordinate system. An equation for any straight line is called a linear equation. The straight-line equation’s general formula is y=mx+a, where m is the straight-line slope, and b is the y-intercept of the line. Linear equations are also first-degree equations as they have the highest exponent value of variables as 1.  

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  • 2x – 3 = 0, 
  • 2y = 8
  •  m + 1 = 0,
  •  y/2 = 3
  •  x + y = 4
  • 3x – y + z = 3

Understanding Linear Equations

Linear Equations are a variety of different equations together. There can be linear equations in one variable, linear equations in two variables, and much more. In every linear equation, one thing remains constant, that the highest degree of all the variables in the equation should always be 1. Other than that, zero-degree variables can also be there. Cuemath can help you get an in-depth understanding of Linear equations through its online learning classes. Cuemath.com is an online learning platform that makes math interesting and engaging by encouraging students to understand ‘why behind the what.’

Linear Equation: Formulas

Linear equation formulas are based on the number of variables used by themselves. First, the variables should be independent and individualistic of each other. Suppose you have y as the variable, then you can’t use y2 as another variable. 

Linear Equation: Graph

The graph of a linear equation in one variable y forms a vertical line parallel to the x-axis and vice-versa. In contrast, the graph of a linear equation in two variables, x, and y forms a straight and horizontal line. The reason an equation of degree one is called a linear equation is that it is a graphical representation of a straight line. 

Some important points to remember in Linear Equations,

  1. The values of the variables that make a linear equation true are called the solution or root of the linear equation.
  2. The solution of any linear equation is unaffected if the same number is added, subtracted, multiplied, or divided into both sides of any equation.
  3. The graph of a linear equation in one or two variables is always a straight line.

Why are they called a Linear Equation? 

They are called linear equations because if you try to plot the graph of the respective equation with variables x and y on a graph with the axis as x and y, you will get a straight line as your result. Hence, they are known as linear equations. 

Forms of a Linear Equation

There are many forms through which a given line is defined in an X-Y place. Some of the common and frequent forms used here for solving any linear equations are:

  • General Form
  • Slope Intercept Form
  • Point Form
  • Intercept Form
  • Two-Point form

What is a common difference between linear and non-linear equations?

A linear equation is meant for only straight lines and not slopes. Simultaneously, a non-linear equation does not form a straight line and can be a curve that has a variable slope value.

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One should understand the basics of linear equations and then move on to complex topics. Linear equations build a solid foundation for geometry. Linear equations will allow students to connect mapping objects in their curriculum to real-world contexts regarding direction and places. Understanding geometrical and graphical relationships is also considered important in the role of problem-solving. They also boost your logical thinking and reasoning skills.