document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150343>Question 150343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> mam/ser,\r<BR>\n" );
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document.write( "please help me to take an advantage about parallel and perpendicular lines..this is my question..<BR>\n" );
document.write( "what is the shortcut methods of the parallel and perpendicular equation?<BR>\n" );
document.write( "i hope you must response...<BR>\n" );
document.write( "                                                       arvy rose juganas </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110325 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> please help me to take an advantage about parallel and perpendicular lines..this is my question..<BR>\n" );
document.write( "what is the shortcut methods of the parallel and perpendicular equation?<BR>\n" );
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document.write( "Not sure what you mean by a \"shortcut method\", however:<BR>\n" );
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document.write( "Parallel line have the same slope:<BR>\n" );
document.write( "in the form y = mx + y (m=slope)<BR>\n" );
document.write( "An example; m=+.4<BR>\n" );
document.write( "y = .4x + 4<BR>\n" );
document.write( "and<BR>\n" );
document.write( "y = .4x - 2<BR>\n" );
document.write( "These lines are parallel because the slope is .4 in both cases, as you can see<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+.4x%2B4%2C+.4x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+.4x%2B4%2C+.4x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Perpendicular lines the relationship: m1 * m2 = -1<BR>\n" );
document.write( "An example:<BR>\n" );
document.write( " the 1st equation slope; m1 = -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 5<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Calculate the slope of the 2nd equation using the above relationship<BR>\n" );
document.write( "-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * m2 = -1<BR>\n" );
document.write( "m2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m2 = +2<BR>\n" );
document.write( "2nd equation: y = 2x+5<BR>\n" );
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document.write( "Looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-.5x%2B5%2C+2x%2B5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-.5x%2B5%2C+2x%2B5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
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