The straight line equation has oblique section: y==kx+m
Point-skew type: y-y0==k (x-x0)
Intercept type: x/a+y/b==1
Two-point formula: (x-x1)/(x2-x1)==(y-y1)/(y2-y1)
How to unify the above form into general equation form: Ax+By+c==0
The actual example is:
y==3x+6
x/3+y/6==1
y-8==2(x-3)
(x-2)/(7-2)==(y-1)/(9-1)
6x+8y+10==0
-x+7y+10==0
The above is unified into the form of Ax+By+C==0
The coefficient in front of x is required to be positive, and the constant terms of x and y are the simplest integers.
6x+8y+10==0 Its final result is 3x+4y+5==0
-x+7y+10==0 Its final result is x-7y-10==0
y=3x+6
should have beeny==3x+6
and likewise for the rest $\endgroup$CoefficientArrays
, see e.g. 185668. For instance{1, x, y} . Flatten@CoefficientArrays[#, {x, y}] & /@ eqs
$\endgroup$