document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=644646>Question 644646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question states: Find an equation for the line.\r<BR>\n" );
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document.write( "4.  through (-8,8) and parallel to y = 3/2x -3.  I have a test on tuesday and cant figure out the steps to work this problem out.  Can you please help me.\r<BR>\n" );
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document.write( "5.  through (-3,8) and vertical\r<BR>\n" );
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document.write( "6.  through (-7,5) and perpendicular to y=2/3x -2\r<BR>\n" );
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document.write( "Can someone walk me through the steps in solving these questions.  Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #405199 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=405199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4.  through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F2%29x+-3 ALIGN=MIDDLE  ALT=\"y+=+%283%2F2%29x+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=equation_parallel_or_perpendicular.solver>Finding the Equation of a Line Parallel or Perpendicular to a Given Line</A></TD></TR>\n" );
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document.write( "  Since any two parallel lines have the same slope we know the slope of the unknown line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (its from the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (-8,8), we can find the equation by plugging in this info into the point-slope formula<BR>\n" );
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document.write( "  Point-Slope Formula:<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;\" > where m is the slope 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;\" >,<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;\" >) is the given point<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=1.5%2A%28x%2B8%29 ALIGN=MIDDLE  ALT=\"y-8=1.5%2A%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1.5 ALIGN=MIDDLE  ALT=\"m=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-8 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=8 ALIGN=MIDDLE  ALT=\"y%5B1%5D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=1.5%2Ax-%281.5%29%28-8%29 ALIGN=MIDDLE  ALT=\"y-8=1.5%2Ax-%281.5%29%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=1.5%2Ax%2B12 ALIGN=MIDDLE  ALT=\"y-8=1.5%2Ax%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax%2B12%2B8 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax%2B12%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate y<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax%2B20 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms<BR>\n" );
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document.write( "   So the equation of the line that is parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax%2B20 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So here are the graphs of the equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax%2B20 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-13%2C5%2C-8%2C13%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-13%2C5%2C-8%2C13%2C+1.5%2Ax%2B-3%2C+1.5%2Ax%2B20%29%2C%0D%0A+++++++++++circle%28-8%2C8%2C0.05%29%2C%0D%0A+++++++++++circle%28-8%2C8%2C0.08%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and graph of the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax%2B20 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green) that is parallel to the given graph and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "5.  through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical ALIGN=MIDDLE  ALT=\"vertical\"   DISABLED_style= \"max-width:90%; height:auto;\" >... I guess to line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F2%29x+-3 ALIGN=MIDDLE  ALT=\"y+=+%283%2F2%29x+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=equation_parallel_or_perpendicular.solver>Finding the Equation of a Line Parallel or Perpendicular to a Given Line</A></TD></TR>\n" );
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document.write( "  Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can find the perpendicular slope by this formula:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2Fm ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D ALIGN=MIDDLE  ALT=\"m%5Bp%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2F%281.5%2F1%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%281.5%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So plug in the given slope to find the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=%28-1%2F1%29%281%2F1.5%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%281%2F1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > When you divide fractions, you multiply the first fraction (which is really <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;\" >) by the reciprocal of the second<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-0.666666666666667%2F1 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-0.666666666666667%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fractions.<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=-0.666666666666667 ALIGN=MIDDLE  ALT=\"-0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So now we know the slope of the unknown line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.666666666666667 ALIGN=MIDDLE  ALT=\"-0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" > (its the negative reciprocal of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (-3,8), we can find the equation by plugging in this info into the point-slope formula<BR>\n" );
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document.write( "  Point-Slope Formula:<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;\" > where m is the slope 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;\" >,<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;\" >) is the given point<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-0.666666666666667%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y-8=-0.666666666666667%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-0.666666666666667 ALIGN=MIDDLE  ALT=\"m=-0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-3 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=8 ALIGN=MIDDLE  ALT=\"y%5B1%5D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-0.666666666666667%2Ax%2B%280.666666666666667%29%28-3%29 ALIGN=MIDDLE  ALT=\"y-8=-0.666666666666667%2Ax%2B%280.666666666666667%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.666666666666667 ALIGN=MIDDLE  ALT=\"-0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-0.666666666666667%2Ax-2 ALIGN=MIDDLE  ALT=\"y-8=-0.666666666666667%2Ax-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.666666666666667%2Ax-2%2B8 ALIGN=MIDDLE  ALT=\"y=-0.666666666666667%2Ax-2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate y<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.666666666666667%2Ax%2B6 ALIGN=MIDDLE  ALT=\"y=-0.666666666666667%2Ax%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms<BR>\n" );
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document.write( "   So the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.666666666666667%2Ax%2B6 ALIGN=MIDDLE  ALT=\"y=-0.666666666666667%2Ax%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So here are the graphs of the equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.666666666666667%2Ax%2B6 ALIGN=MIDDLE  ALT=\"y=-0.666666666666667%2Ax%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-8%2C5%2C-8%2C13%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-8%2C5%2C-8%2C13%2C+1.5%2Ax%2B-3%2C+-0.666666666666667%2Ax%2B6%29%2C%0D%0A+++++++++++circle%28-3%2C8%2C0.05%29%2C%0D%0A+++++++++++circle%28-3%2C8%2C0.08%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.5%2Ax-3 ALIGN=MIDDLE  ALT=\"y=1.5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and graph of the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.666666666666667%2Ax%2B6 ALIGN=MIDDLE  ALT=\"y=-0.666666666666667%2Ax%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >(green) that is perpendicular to the given graph and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "6.  through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x+-2 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=equation_parallel_or_perpendicular.solver>Finding the Equation of a Line Parallel or Perpendicular to a Given Line</A></TD></TR>\n" );
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document.write( "  Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.666666666666667 ALIGN=MIDDLE  ALT=\"0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can find the perpendicular slope by this formula:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2Fm ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D ALIGN=MIDDLE  ALT=\"m%5Bp%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=-1%2F%280.666666666666667%2F1%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%280.666666666666667%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So plug in the given slope to find the perpendicular slope<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bp%5D=%28-1%2F1%29%281%2F0.666666666666667%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%281%2F0.666666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > When you divide fractions, you multiply the first fraction (which is really <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;\" >) by the reciprocal of the second<BR>\n" );
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document.write( " I think you can't see everything here and I will write remaining part:\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%2F2 ALIGN=MIDDLE  ALT=\"m=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So now we know the slope of the unknown line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F2 ALIGN=MIDDLE  ALT=\"m=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (its the negative reciprocal of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x-2 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also since the unknown line goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can find the equation by plugging in this info into the point-slope formula\r<BR>\n" );
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document.write( "Point-Slope Formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y1=m%28x-x%29 ALIGN=MIDDLE  ALT=\"y-y1=m%28x-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where m is the slope and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1 ALIGN=MIDDLE  ALT=\"x1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y1 ALIGN=MIDDLE  ALT=\"y1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is the given point\r<BR>\n" );
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document.write( "So the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x-2 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F2%29x-11%2F2 ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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