document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118671>Question 118671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation that is parrallel and perpendicular to the given line.<BR>\n" );
document.write( "y=-1/3x+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86800 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=86800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An equation that is parallel has the same slope. So the slope of this parallel line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F3 ALIGN=MIDDLE  ALT=\"m=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now just replace the 2 with any number such as 5 to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29x%2B5 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So one parallel line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29x%2B5 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice if we graph the two equations, we can see that they are parallel. So this verifies our answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C%28-1%2F3%29x%2B5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C%28-1%2F3%29x%2B5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29x%2B5 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
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document.write( "An equation that is perpendicular has an negated inverted slope. Since the original slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F3 ALIGN=MIDDLE  ALT=\"m=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fm=-1%2F%28-1%2F3%29=%28-1%2F1%29%2A%28-3%2F1%29=3%2F1=3 ALIGN=MIDDLE  ALT=\"-1%2Fm=-1%2F%28-1%2F3%29=%28-1%2F1%29%2A%28-3%2F1%29=3%2F1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   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=3x%2B2 ALIGN=MIDDLE  ALT=\"y=3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now just replace the slope of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F3 ALIGN=MIDDLE  ALT=\"m=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the new slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get a perpendicular line.\r<BR>\n" );
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document.write( "So one perpendicular line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B2 ALIGN=MIDDLE  ALT=\"y=3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice if we graph the two equations, we can see that they are perpendicular. So this verifies our answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C3x%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C3x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B2 ALIGN=MIDDLE  ALT=\"y=3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) </SPAN>\n" );
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