document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442577>Question 442577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line containing the given point and perpendicular to give line for:<BR>\n" );
document.write( "(7,-7);7x+2y=5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305290 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=305290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (7,-7)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-7x%2B5 ALIGN=MIDDLE  ALT=\"2y=-7x%2B5\"   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=-%287%2F2%29x%2B5%2F5 ALIGN=MIDDLE  ALT=\"y=-%287%2F2%29x%2B5%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=y=-%283.5%29x%2B2.5 ALIGN=MIDDLE  ALT=\"y=-%283.5%29x%2B2.5\"   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=-3.5 ALIGN=MIDDLE  ALT=\"-3.5\"   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%28-3.5%2F1%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%28-3.5%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%2F-3.5%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%281%2F-3.5%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%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=0.666666666666667%2F2.33333333333333\"   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%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"0.666666666666667%2F2.33333333333333\"   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%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"0.666666666666667%2F2.33333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" > (its the negative reciprocal of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3.5 ALIGN=MIDDLE  ALT=\"-3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3.5%2Ax%2B2.5 ALIGN=MIDDLE  ALT=\"y=-3.5%2Ax%2B2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (7,-7), 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%2B7=%280.666666666666667%2F2.33333333333333%29%2A%28x-7%29 ALIGN=MIDDLE  ALT=\"y%2B7=%280.666666666666667%2F2.33333333333333%29%2A%28x-7%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%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"m=0.666666666666667%2F2.33333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=7 ALIGN=MIDDLE  ALT=\"x%5B1%5D=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-7 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-7\"   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%2B7=%280.666666666666667%2F2.33333333333333%29%2Ax-%280.666666666666667%2F2.33333333333333%29%287%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.666666666666667%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"0.666666666666667%2F2.33333333333333\"   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%2B7=%280.666666666666667%2F2.33333333333333%29%2Ax-4.66666666666667%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"y%2B7=%280.666666666666667%2F2.33333333333333%29%2Ax-4.66666666666667%2F2.33333333333333\"   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=%280.666666666666667%2F2.33333333333333%29%2Ax-4.66666666666667%2F2.33333333333333-7 ALIGN=MIDDLE  ALT=\"y=%280.666666666666667%2F2.33333333333333%29%2Ax-4.66666666666667%2F2.33333333333333-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > from 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=%280.666666666666667%2F2.33333333333333%29%2Ax-4.66666666666667%2F2.33333333333333-16.3333333333333%2F2.33333333333333 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Make into equivalent fractions with equal denominators<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce any fractions<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=-3.5%2Ax%2B2.5 ALIGN=MIDDLE  ALT=\"y=-3.5%2Ax%2B2.5\"   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=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333\"   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=-3.5%2Ax%2B2.5 ALIGN=MIDDLE  ALT=\"y=-3.5%2Ax%2B2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333\"   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+-5%2C12%2C-12%2C7.5%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-5%2C12%2C-12%2C7.5%2C+-3.5%2Ax%2B2.5%2C+0.285714285714286%2Ax%2B-9%29%2C%0D%0A+++++++++++circle%287%2C-7%2C0.05%29%2C%0D%0A+++++++++++circle%287%2C-7%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=-3.5%2Ax%2B2.5 ALIGN=MIDDLE  ALT=\"y=-3.5%2Ax%2B2.5\"   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=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333 ALIGN=MIDDLE  ALT=\"y=%280.666666666666667%2F2.33333333333333%29%2Ax-21%2F2.33333333333333\"   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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "so, the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.28x+-+0.86 ALIGN=MIDDLE  ALT=\"y=0.28x+-+0.86\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283.5%29x%2B2.5 ALIGN=MIDDLE  ALT=\"y=-%283.5%29x%2B2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and containing the given point (7,-7) </SPAN>\n" );
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