document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175268>Question 175268</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078457718/algebrahomeworkh>Glencoe Algebra Concepts and Applications</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the graphs of each pair of equations are parallel,perpendicular, or neither. 23) 7x+3y=4    <BR>\n" );
document.write( "                3x-7y=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130356 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=130356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B3y=4 ALIGN=MIDDLE  ALT=\"7x%2B3y=4\"   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=3y=4-7x ALIGN=MIDDLE  ALT=\"3y=4-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x ALIGN=MIDDLE  ALT=\"7x\"   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=3y=-7x%2B4 ALIGN=MIDDLE  ALT=\"3y=-7x%2B4\"   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=%28-7x%2B4%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y=%28-7x%2B4%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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%28-7%29%2F%283%29%29x%2B%284%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y=%28%28-7%29%2F%283%29%29x%2B%284%29%2F%283%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=-%287%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=-%287%2F3%29x%2B4%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=-%287%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=-%287%2F3%29x%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-7%2F3 ALIGN=MIDDLE  ALT=\"m=-7%2F3\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-7y=1 ALIGN=MIDDLE  ALT=\"3x-7y=1\"   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=-7y=1-3x ALIGN=MIDDLE  ALT=\"-7y=1-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   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=-7y=-3x%2B1 ALIGN=MIDDLE  ALT=\"-7y=-3x%2B1\"   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=%28-3x%2B1%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"y=%28-3x%2B1%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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%28-3%29%2F%28-7%29%29x%2B%281%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"y=%28%28-3%29%2F%28-7%29%29x%2B%281%29%2F%28-7%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=%283%2F7%29x-1%2F7 ALIGN=MIDDLE  ALT=\"y=%283%2F7%29x-1%2F7\"   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=%283%2F7%29x-1%2F7 ALIGN=MIDDLE  ALT=\"y=%283%2F7%29x-1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3%2F7 ALIGN=MIDDLE  ALT=\"m=3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1%2F7 ALIGN=MIDDLE  ALT=\"b=-1%2F7\"   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=-7%2F3 ALIGN=MIDDLE  ALT=\"m=-7%2F3\"   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=3%2F7 ALIGN=MIDDLE  ALT=\"m=3%2F7\"   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=3%2F7 ALIGN=MIDDLE  ALT=\"m=3%2F7\"   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=-7%2F3 ALIGN=MIDDLE  ALT=\"m=-7%2F3\"   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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%287%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=-%287%2F3%29x%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F7%29x-1%2F7 ALIGN=MIDDLE  ALT=\"y=%283%2F7%29x-1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > are perpendicular lines.<BR>\n" );
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