document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486001>Question 486001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let (x1, y1)=(-6,-3) and (x2,y2)=(-4,5). Find y2-y1/x2-x1 and y1-y2/x1-x2 are the results the same?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332304 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Better than that, let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_1,y_1)\ =\ (a,c)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_2,y_2)\ =\ (b,d)\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y_2\ -\ y_1}{x_2\ -\ x_1}\ =\  \frac{d\ -\ c}{b\ -\ a}\">.\r<BR>\n" );
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document.write( "Factor -1 from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (d\ -\ c)\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ -\ c\ =\ (-1)(-d\ +\ c)\ =\ (-1)(c\ -\ d)\">\r<BR>\n" );
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document.write( "Likewise:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ -\ a\ =\ (-1)(-b\ +\ a)\ =\ (-1)(a\ -\ b)\">\r<BR>\n" );
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document.write( "So, by substitution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y_2\ -\ y_1}{x_2\ -\ x_1}\ =\  \frac{(-1)(c\ -\ d)}{(-1)(a\ -\ b)}\">.\r<BR>\n" );
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document.write( "But since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{-1}{-1}\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(-1)(c\ -\ d)}{(-1)(a\ -\ b)}\ =\ \frac{c\ -\ d}{a\ -\ b}\">.\r<BR>\n" );
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document.write( "But\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y_1\ -\ y_2}{x_1\ -\ x_2}\ =\  \frac{c\ -\ d}{a\ -\ b}\">.\r<BR>\n" );
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document.write( "also.  Therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y_1\ -\ y_2}{x_1\ -\ x_2}\ =\ \frac{y_2\ -\ y_1}{x_2\ -\ x_1}\ \forall x_i,\,y_i\ \in\ \mathbb{R},\ x_1\ \neq\ x_2\\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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