BTGmoderatorDC wrote:If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?
(1) A = 2B
(2) C = 4B
Source: Magoosh
Important: from the stem we know (implicitly) that line k HAS a slope, i.e., line k is non-vertical, i.e., B is nonzero.
$$Ax + By = C\,\,\,\,\,\mathop \Leftrightarrow \limits^{B\,\, \ne \,\,0} \,\,\,y\,\, = - {A \over B}\left( x \right)\,\, + \,\,{C \over A}$$
$$? = - {A \over B}$$
$$\left( 1 \right)\,\,\,A = 2B\,\,\,\,\mathop \Rightarrow \limits^{B\,\, \ne \,\,0} \,\,\,\,\,? = - {A \over B} = - 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,\,C = 4B\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {A,B,C} \right) = \left( {1,1,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{?}}\,\,\,{\rm{ = }}\,\, - 1\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {A,B,C} \right) = \left( {2,1,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{?}}\,\,\,{\rm{ = }}\,\, - 2\,\, \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
