Problem Solving

Brent@GMATPrepNow wrote:In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
Source: www.gmatprepnow.com

Reminder (to my students) / Suggestion (to the general reader):

1. One property at a time, till the end. Then the other. ("Don´t let your brain dance!")

2. Start with the easier checking property (or the one you feel more comfortable).
Indifferent? Start with the first.
\[?\,\,\left( 1 \right)\,\,\,\,:\,\,\,\,\left( {5, - 4} \right)\,\,\mathop \in \limits^? \,\,\,{\text{line}}\,\,\]
\[\left( i \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{2}{5}\left( 5 \right) - 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\]
\[\left( {ii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{6}{5}\left( 5 \right) + 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\]
\[\left( {iii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{7}{{10}}\left( 5 \right) - \frac{3}{2}\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( C \right),\,\,\left( E \right)\]
\[?\,\,\left( 2 \right)\,\,\,\,:\,\,\,\,{\text{line}}\,\,x - {\text{intercept}}\,\,\,\mathop < \limits^? \,\,0\]
\[\left( i \right)\,\,0\, = \,\, - \frac{2}{5}\left( x \right) - 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( B \right)\]
\[\left( {ii} \right)\,\,0\, = \,\, - \frac{6}{5}\left( x \right) + 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( D \right)\]

The correct answer is (A).

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.