document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166670>Question 166670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graphs of equations perpendicular, parallel or neither<BR>\n" );
document.write( "6x+5y=3<BR>\n" );
document.write( "5x-6y=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122838 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=122838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5y=3 ALIGN=MIDDLE  ALT=\"6x%2B5y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=3-6x ALIGN=MIDDLE  ALT=\"5y=3-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=-6x%2B3 ALIGN=MIDDLE  ALT=\"5y=-6x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-6x%2B3%29%2F%285%29 ALIGN=MIDDLE  ALT=\"y=%28-6x%2B3%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-6%29%2F%285%29%29x%2B%283%29%2F%285%29 ALIGN=MIDDLE  ALT=\"y=%28%28-6%29%2F%285%29%29x%2B%283%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2F5%29x%2B3%2F5 ALIGN=MIDDLE  ALT=\"y=-%286%2F5%29x%2B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So we can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2F5%29x%2B3%2F5 ALIGN=MIDDLE  ALT=\"y=-%286%2F5%29x%2B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-6%2F5 ALIGN=MIDDLE  ALT=\"m=-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3%2F5 ALIGN=MIDDLE  ALT=\"b=3%2F5\"   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=5x-6y=8 ALIGN=MIDDLE  ALT=\"5x-6y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now move onto the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6y=-5x%2B8 ALIGN=MIDDLE  ALT=\"-6y=-5x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5x%2B8%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"y=%28-5x%2B8%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-5%29%2F%28-6%29%29x%2B%288%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"y=%28%28-5%29%2F%28-6%29%29x%2B%288%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F6%29x-4%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So we can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F6%29x-4%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5%2F6 ALIGN=MIDDLE  ALT=\"m=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-4%2F3 ALIGN=MIDDLE  ALT=\"b=-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the slope of the first line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-6%2F5 ALIGN=MIDDLE  ALT=\"m=-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the slope of the second line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5%2F6 ALIGN=MIDDLE  ALT=\"m=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice how the slope of the second line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=5%2F6 ALIGN=MIDDLE  ALT=\"m=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is simply the negative reciprocal of the slope of the first line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-6%2F5 ALIGN=MIDDLE  ALT=\"m=-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope. So this means that the graphs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2F5%29x%2B3%2F5 ALIGN=MIDDLE  ALT=\"y=-%286%2F5%29x%2B3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F6%29x-4%2F3 ALIGN=MIDDLE  ALT=\"y=%285%2F6%29x-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > are perpendicular lines.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Consequently, this means that the graphs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5y=3 ALIGN=MIDDLE  ALT=\"6x%2B5y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-6y=8 ALIGN=MIDDLE  ALT=\"5x-6y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > are perpendicular lines. </SPAN>\n" );
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