The common method is to use the determinant
A(48,7) B(93,84)
The vector formed by A and B is :
vec(AB) = (93-48,84-7) = (45,77)
(which is a vector director to our line)
and now imagine a point M(x,y) it can be anything
the vector formed by A and M is ;
vec(AM) = (x-48,y-7)
vec(AB) and vec(AM) are parallel if and only if det(vec(AB),vec(AM)) = 0
in fact they will be parallel and be on the same line, because they share the same point A
Why if det(vec(AB),vec(AM)) = 0 they are parallel ?
because det(vec(AB),vec(AM)) = AB*AMsin(theta) where theta is the angle formed by the two vectors, since the vectors are not = vec(0) the only way det(vec(AB),vec(AM)) = 0 it is sin(theta) = 0
and sin(theta) = 0 when theta = pi or = 0 if the angle between two line =0 or = pi they are parallel (Euclide definition)
compute the det and find
45(y-7) - 77(x-48) = 0
And voilà ! You know how to do it geometrically ; )
