The "Standard form" for a linear equation:
Ax + By = C, where (1) A should not be negative, (2) A and B shouldn't be zero, and (3) A, B, C should be integers.
Similarly, Ax + By + C = 0 is called the "General form".
y - 3 = 4/7 (x - 1)
7(y - 3) = 4(x - 1)
7y - 21 = 4x - 4
-4x + 7y = -4 + 21
4x - 7y = -17