A Linear equation is a part of algebra in mathematics. In a linear equation, each term is a constant or it can be a product of constant of the variable. A very simple equation that can be written with one variable (x) could be ax + b=0, where a and b are constant and a ≠ 0. The constants a and b could be any numbers or parameters. Linear equations are universal in the applications of mathematics. Those equations that involve single variable will appear in simplest problems wherein one unknown parameter or quantity has to be solved from the other information which is given. In solving simple equations, one needs to use only elementary operations of arithmetic such as addition, multiplication, subtraction, and division. How to solve linear equations?One can solve the linear equations with visualization which is the ability or the process, and the product of the creation, use of, interpretation, and reflection which is used upon the pictures, diagrams, and images in the minds, paper or technological tools. The purpose of the solving is to depict and communicate the information which is thought upon and developed using previously unknown ideas and of advancing understandings. Linear Equations with More Variables:Equations can have one more one variables, such as equation with three variables x, y, and z is written asax + by + cz = 0, wherein a, b, and c are the constants and are any number except zero. Equations with the exponents that are greater than one are known as non – linear equations. For example, axy + b = 0, where a and b are constants and a is not equal to zero. The equation has two variables x and y and is said to be non – linear as the sum of the exponents of the two variables in the first term is two. Forms of Two – Dimensional Linear EquationsThere are different forms in which the linear equations can be written. These are: - General Form – In this, the equation is written as Ax + By = C, where a and b are not equal to zero. The graph plotted is in a straight line.
- Slope – Intercept form – The equation is written as y = mx + b, where m is the slope of line and b, the intercept of y, that is the y coordinate of location wherein the line crosses the y-axis.
- Point – slope form – The equation is written as y – y1 = y2-y1/ x2 – x1 (x – x1), wherein (x1, y1) and (x2, y2) are the two points on line with x2 ≠ x1. The equation is also known as symmetrical form as when both the sides are multiplied it yields a form of the line which is in symmetry.
- Intercept Form – The equation is written as x/a + y/b = 1, where a and b must not be equal to zero. The graph of intercept form equation has x and y-intercept as a and b, respectively.
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