document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=260766>Question 260766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine whether the line is PQ is parallel or perpendicular to line with a slope of -2.\r<BR>\n" );
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document.write( "P(5,6)<BR>\n" );
document.write( "Q (9,8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192107 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=192107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> determine whether the line is PQ is parallel or perpendicular to line with a slope of -2.\r<BR>\n" );
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document.write( "P(5,6)<BR>\n" );
document.write( "Q (9, 8)\r<BR>\n" );
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document.write( "Ok, here are two things you have to know:\r<BR>\n" );
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document.write( "If lines are PARALLEL, they have the SAME slope.<BR>\n" );
document.write( "If lines are PERPENDICULAR, their slopes are negative reciprocals of one another. In other words, if one slope is 2 the negative reciprocal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F2 ALIGN=MIDDLE  ALT=\"%28-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.    If one slope is -2, then the negative reciprocal is <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;\" >.\r<BR>\n" );
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document.write( "Ok, so you are given that you have a line with a slope of -2.  Next you are asked if line PQ is parallel or perpendicular to the line with a slope of -2.\r<BR>\n" );
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document.write( "Ok, let's just find the slope for line PQ.  The way to find slope is to use this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B1%5D+-+y%5B2%5D%29 ALIGN=MIDDLE  ALT=\"%28y%5B1%5D+-+y%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D+-+x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D+-+x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's plug in the info from PQ\r<BR>\n" );
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document.write( "P(5,6)<BR>\n" );
document.write( "Q (9, 8)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+-+8 ALIGN=MIDDLE  ALT=\"6+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+-+9 ALIGN=MIDDLE  ALT=\"5+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%28-2%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4 ALIGN=MIDDLE  ALT=\"2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which reduces to<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;\" ><BR>\n" );
document.write( "The slope of line PQ is:  <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;\" >\r<BR>\n" );
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document.write( "The slope we were given was -2.  The slope of PQ is <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;\" >.  Therefore, because <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;\" > is the negative reciprocal of -2, the two lines are PERPENDICULAR.\r<BR>\n" );
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document.write( "If you get nervous about the use of negative reciprocals, just do one final check. Multiply the first slope times the 2nd.  If the answer is -1, then the slopes are indeed negative reciprocals of one another.\r<BR>\n" );
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document.write( "So let's do that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2F1 ALIGN=MIDDLE  ALT=\"%28-2%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > x <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2F2 ALIGN=MIDDLE  ALT=\"%28-2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F1 ALIGN=MIDDLE  ALT=\"%28-1%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is -1.\r<BR>\n" );
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document.write( "Ok, that's your final check. The lines are perpendicular.\r<BR>\n" );
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document.write( "I hope this helps you. :-) </SPAN>\n" );
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