document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158073>Question 158073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this one.<BR>\n" );
document.write( "Determine whether the graphs of the equations are parallel lines, perpendicular lines or niether.<BR>\n" );
document.write( "3x - 8y =  -18<BR>\n" );
document.write( "32x + 12y = -18<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116466 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To determine whether the graphs of the given equations are perpendicular lines, parallel lines, or neither, you need ony to compare their slopes.<BR>\n" );
document.write( "Perpendicular lines have negative reciprocal slopes.<BR>\n" );
document.write( "Parallel lines have equal slopes, and neither have neither!<BR>\n" );
document.write( "So, let's get the equations into their \"slope-intercept\" forms: y=mx+b.<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-8y+=+-18 ALIGN=MIDDLE  ALT=\"3x-8y+=+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 8y to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+8y-18 ALIGN=MIDDLE  ALT=\"3x+=+8y-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 18 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B18+=+8y ALIGN=MIDDLE  ALT=\"3x%2B18+=+8y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 8.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+=+%283%2F8%29x%2B9%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28y+=+%283%2F8%29x%2B9%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > The slope here is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m%5B1%5D+=+3%2F8%29 ALIGN=MIDDLE  ALT=\"highlight%28m%5B1%5D+=+3%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32x%2B12y+=+-18 ALIGN=MIDDLE  ALT=\"32x%2B12y+=+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y+=+-32x-18 ALIGN=MIDDLE  ALT=\"12y+=+-32x-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 12.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+=+%28-8%2F3%29x-9%2F6%29 ALIGN=MIDDLE  ALT=\"highlight%28y+=+%28-8%2F3%29x-9%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > The slope here is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m%5B2%5D+=+-8%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28m%5B2%5D+=+-8%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D+=+3%2F8 ALIGN=MIDDLE  ALT=\"m%5B1%5D+=+3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D+=+-8%2F3 ALIGN=MIDDLE  ALT=\"m%5B2%5D+=+-8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can see that they are negative reciprocals and, therefore, their graphs of the equations will be perpendicular lines.<BR>\n" );
document.write( "For confirmation, we'll graph the two equations. Red = equation 1). Green = equation 2).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-8%2C5%2C-5%2C8%2C%283%2F8%29x%2B%289%2F4%29%2C%28-8%2F3%29x-%289%2F6%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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