Line Equation

A line equation is nothing but an algebraic equation where every term in that equation will either be a product of a constant and a single variable or simply a constant. These equations will have one or more than one variables. They play an important role in applied mathematics. Equation of a line may simply be said as the linear equation which will not include exponents. In modeling many phenomenons, these equations are used in reducing non linear equations to linear equations from the assumption that the interested quantities will vary from background state only to a small extent.

The most common form used in order to find an equation of a line is given by, Y= mx + b.

The above given equation is used to describe the straight line on a particular coordinate plane. There are many equations representing the equation of a straight line, but this is the common form. This representation is known as Slope and Intercept form. In above said equation, ‘x’ and ‘y’ represents the coordinates of any points lying on the line, ‘m’ is known as the slope of the line(steepness) and ‘b’ is known as the Intercept which is a point formed when the line is crossing the y axis.

Standard Form Line Equation
There are many ways in order to express the equation of a line which are having their own pros and cons. There is a standard form in order to represent the equation of the line, which is given as Ax + By = C, where both A and B are not equal to zero. The equation finally is represented in this form giving out the standard form to represent. This standard form is essential when one needs to graph out the line or in order to find the line y intercept or x intercept. Also, some of the other forms for finding equation of a line are given as follows:

• Point-slope form: y – y1 = m(x-x1), where x1 and y1 are any points present on the line and ‘m’ is the slope, which is nothing but the proportionality constant. 
• Two point form: When there are two points lying on the line, then the formula to find the equation of the line is (x2–x1) (y-y1) = (y2-y1) (x-x1). Here x1, y1 and x2, y2 are two points present on the line, where x1 and x2 are not equal. Here the value y2-y1 divided by x2-x1 is nothing but the slope formula, which when simplified will give the point slope form. 
• Intercept form: This equation is a modification of standard form, where A is 1 divided by ‘a’ and B is 1 divided by ‘b’. This equation states that the sum of x divided by ‘a’ and y divided by ‘b’ will be equal to one.