Question 890086
<font face="Times New Roman" size="+2">


There is no real number *[tex \Large c] such that a line with slope *[tex \Large c] contains the points *[tex \Large (1, 8)] and *[tex \Large (c, 2)]


The slope of a line containing the points *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] is given by *[tex \Large m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} ].


Substituting what you were given, you get:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c\ =\ \frac{2\ -\ 8}{c\ -\ 1} ]


Then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c^2\ -\ c\ +\ 6\ =\ 0]


giving us a quadratic in *[tex \Large c].  A little arithmetic shows that the discriminant is negative, hence there are no real values of *[tex \Large c] that satisfy the parameters of the problem.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>