The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.
Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.
Slope of line taking points (X1,Y1) and (X2,Y2) is
 ........................(1)
Slope of line taking points (X3,Y3) and (X1,Y1) is
 ........................(2)
From conditions (1) and (2)
The 3 points do not a same line.
For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.
Here the slopes are unequal hence the points do not lie on same line.
To read more on equations of a line refer to articles on wikipedia
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