Respuesta :
La ecuación general de estas ecuaciones continuas es de la siguiente forma:
[tex]\boxed{\boxed{\boldsymbol{\mathsf{Ax+By+C=0}}}}[/tex]
Para llegar a esto solo multiplicaremos en aspa y trasladaremos a un solo miembro los términos, entonces
A.
[tex]\center \mathsf{\dfrac{x - 4}{-1} = \dfrac{y - 2}{2}}\\\\\center \mathsf{(2)(x - 4) = (-1)(y - 2)}\\\\\center \mathsf{2x - 8 = -y + 2}\\\\\center \mathsf{2x - 8 + y - 2 = 0}\\\\\center \boxed{\boldsymbol{\mathsf{2x + y - 10 = 0}}} \Rightarrow \mathsf{Ec. general }[/tex]
B.
[tex]\center \mathsf{\dfrac{x - 2}{3} = \dfrac{y - 3}{7}}\\\\\center \mathsf{(7)(x - 2) = (3)(y - 3)}\\\\\center \mathsf{7x - 14 = 3y - 9}\\\\\center \mathsf{7x - 14 - 3y + 9 = 0}\\\\\center \boxed{\boldsymbol{\mathsf{7x - 3y - 5 = 0}}} \Rightarrow \mathsf{Ec. general }[/tex]
C.
[tex]\center \mathsf{\dfrac{x - 1}{-1} = \dfrac{y - 2}{5}}\\\\\center \mathsf{(5)(x - 1) = (-1)(y - 2)}\\\\\center \mathsf{10x - 5 = -y + 2}\\\\\center \mathsf{10x - 5 + y - 2 = 0}\\\\\center \boxed{\boldsymbol{\mathsf{10x + y - 7 = 0}}} \Rightarrow \mathsf{Ec. general }[/tex]
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