document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202834>Question 202834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of the line that contains the point (-4, -10) and is perpendicular to the line that contains the points (-3, 6)and (3, 12) is?\r<BR>\n" );
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document.write( "a. Y= x+9\r<BR>\n" );
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document.write( "b. Y= -x-14\r<BR>\n" );
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document.write( "c. Y= -x+9\r<BR>\n" );
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document.write( "d. Y= 16x+54 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153022 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=153022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of the line that contains the point (-4, -10) and is perpendicular to the line that contains the points (-3, 6)and (3, 12) is? <BR>\n" );
document.write( "a. Y= x+9 <BR>\n" );
document.write( "b. Y= -x-14 <BR>\n" );
document.write( "c. Y= -x+9 <BR>\n" );
document.write( "d. Y= 16x+54\r<BR>\n" );
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document.write( "Ok, let's start this from the idea that the equation of the line must be perpendicular to the points (-3, 6)and (3, 12).   There are two facts you must know to solve this problem:\r<BR>\n" );
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document.write( "1)  Perpendicular lines have slopes that are NEGATIVE reciprocals of one another. That's just a fancy way of saying you \"flip\" them and take the opposite.   Sooo, if your slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a line perpendicular to that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "2)  To find the slope of a line, you follow this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D-y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D-y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "______________<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D-x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D-x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(I am very sorry this fraction does not look nice.  I am not adept yet at making fractions and what-not on this site).  \r<BR>\n" );
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document.write( "So, let's find the slope of these ordered pairs:\r<BR>\n" );
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document.write( "(-3, 6)and (3, 12)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-6 ALIGN=MIDDLE  ALT=\"12-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "__________<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-+-3 ALIGN=MIDDLE  ALT=\"3-+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-6 ALIGN=MIDDLE  ALT=\"12-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "__________<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B3 ALIGN=MIDDLE  ALT=\"3%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F6 ALIGN=MIDDLE  ALT=\"6%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What is the negative reciprocal of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >?  <BR>\n" );
document.write( "The negative reciprocal is:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F1 ALIGN=MIDDLE  ALT=\"-1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or:  -1\r<BR>\n" );
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document.write( "Now we must make sure that the equation of the line includes the point (-4, -10) and must have a slope of -1 if it is to be perpendicular to the line that contains the points (-3, 6)and (3, 12).\r<BR>\n" );
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document.write( "To find this equation of a line, you would need the POINT SLOPE equation of a line.  In other words, you know a point on the line (-4, -10) and you know the slope is -1 sooo, you just fill that info into the point slope equation of a line.  \r<BR>\n" );
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document.write( "Let's look at the POINT SLOPE equation of a line.   In this equation, \"m\" is the slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > refer to a point that the line goes thru.  Here is the point slope equation of a line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now just fill in with this info:<BR>\n" );
document.write( "m = -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-10 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (point slope equation of line)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-++-10+=+-1%28x+-+-4%29 ALIGN=MIDDLE  ALT=\"y+-++-10+=+-1%28x+-+-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (fill in given values, which computes to...)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B10+=+-1%28x%2B4%29 ALIGN=MIDDLE  ALT=\"y+%2B10+=+-1%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (<---which computes to this line)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B10+=+-1x+-+4 ALIGN=MIDDLE  ALT=\"y+%2B10+=+-1x+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (distribute the -1 to the \"x\" and to the 4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1x+-+4+-10 ALIGN=MIDDLE  ALT=\"y+=+-1x+-+4+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (subtract -10 from both sides)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1x+-14 ALIGN=MIDDLE  ALT=\"y+=+-1x+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > (final answer)\r<BR>\n" );
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document.write( "Therefore, your answer is \"b\" which is: b. Y= -x-14 \r<BR>\n" );
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document.write( "I hope this helps you! :-)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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