BTGmoderatorDC wrote:In the xy-coordinate system, line k has slope 1/2 and passes through point (0, 5). Which of the following points cannot lie on line k?
A. (-10, 0)
B. (8, 9)
C. (3, 6.5)
D. (-2, 2)
E. (-8, 1)
\[{\text{line}}\,\,:\,\,\,y = \frac{1}{2}x + 5\]
\[\boxed{\,\,{\text{?}}\,\,\,{\text{:}}\,\,\,{\text{point}}\,\,\left( {a,b} \right)\,\, \notin \,\,{\text{line}}\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,?\,\,\,\,:\,\,\,\,b \ne \frac{a}{2} + 5\,\,\,\,}\]
\[\left( A \right)\,\,\,0\,\,\,\mathop \ne \limits^? \,\,\frac{{ - 10}}{2} + 5\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \]
\[\left( B \right)\,\,\,9\,\,\,\mathop \ne \limits^? \,\,\frac{8}{2} + 5\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \]
\[\left( C \right)\,\,\,6.5\,\,\,\mathop \ne \limits^? \,\,\frac{3}{2} + 5\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \]
\[\left( D \right)\,\,\,2\,\,\,\mathop \ne \limits^? \,\,\frac{{ - 2}}{2} + 5\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
P.S.: in this problem we don´t see any justifiable reason to start the choices evaluation from bottom to the top, with all respect to our colleague's different beliefs.
In short: we see no "scientific" (statistical, information available) arguments for the claim ("the correct answer is typically closer to the bottom than to the top").
(We read the link provided above and, with due respect, we believe the "statistical sample" mentioned there is not significant.)