Line equation through two points

One of the simplest, and most common tasks is to determine the equation that passing through two points.

The solution of a linear equation can be written as an implicit formula as follows:

or with an explicit formula:

First, let the given points be A(x1 ; y1) and B(x2 ; y2).

The underlined equation is fit for both points by definition, so we can write the following two equations:

Subtract the second equation from the first equation:

Subtitute this expression for coefficient „a” into the first equation:

Clearing fractions by multiplication (x1-x2):

Make the coefficient „c” the subject of the formula:

Now subtitute the coefficients „a” and „c” into the first underlined equation:

Clearing denominators by multiplication [(x1-x2)/b]:

Now we can get fractionless expressions for each of the three coefficients of the line equation:

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