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Forma general. A x + B y + C = 0
Forma explícita. y = m x + b
Si representan la misma recta, despejamos y de la primera.
y = (- A x - C) / B = - A/B x - C/B
de modo que m = - A/B; b = - C/B; con B ≠ 0
Saludos Herminio