document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187407>Question 187407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.\r<BR>\n" );
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document.write( "3x-8y=-18<BR>\n" );
document.write( "32x+12y=-18<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140493 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=140493\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  L_1 \parallel L_2 \ \ \Leftrightarrow\ \ m_1 = m_2\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = \frac{-1}{m_2}\">\r<BR>\n" );
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document.write( "So, calculate the slopes.  Since both equations are in standard form, i.e.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ Ax + By = C\">,\r<BR>\n" );
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document.write( "you take the opposite of the coefficient on <i>x</i>, which would be -3 in the case of your first equation, and divide it by the coeffiecient on <i>y</i>, which would be -8 in the case of your first equation.  Do the same thing for your second equation.  If the slopes are equal, the lines are parallel.  If the slopes are negative reciprocals, the lines are perpendicular.  If there is any other relationship between the slopes, then the lines are neither parallel or perpendicular. \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" );
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