document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119821>Question 119821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) how do you write in slope-intercept form of the line that passes through (6,-13) and is perpendicular to the graph 2x-9y=5?\r<BR>\n" );
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document.write( "2) (-3,1), y=1/3x+2\r<BR>\n" );
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document.write( "3) (6,-1), 3y+x=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87810 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=87810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1\r<BR>\n" );
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document.write( "First convert the standard equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9y=5 ALIGN=MIDDLE  ALT=\"2x-9y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > into slope intercept form\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=converting_linear_equations.solver>Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9y=5 ALIGN=MIDDLE  ALT=\"2x-9y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9y-2x=5-2x ALIGN=MIDDLE  ALT=\"2x-9y-2x=5-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9y=-2x%2B5 ALIGN=MIDDLE  ALT=\"-9y=-2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9y%29%2F%28-9%29=%28-2x%2B5%29%2F%28-9%29 ALIGN=MIDDLE  ALT=\"%28-9y%29%2F%28-9%29=%28-2x%2B5%29%2F%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -9 to isolate y<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2x%29%2F%28-9%29%2B%285%29%2F%28-9%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2x%29%2F%28-9%29%2B%285%29%2F%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction on the right hand side<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F9%29x-5%2F9 ALIGN=MIDDLE  ALT=\"y+=+%282%2F9%29x-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce and simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-9y=5 ALIGN=MIDDLE  ALT=\"2x-9y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F9%29x-5%2F9 ALIGN=MIDDLE  ALT=\"y+=+%282%2F9%29x-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F9%29x-5%2F9 ALIGN=MIDDLE  ALT=\"y+=+%282%2F9%29x-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2%2F9 ALIGN=MIDDLE  ALT=\"m=2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5%2F9 ALIGN=MIDDLE  ALT=\"b=-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y intercept.<br><br><br></TD></TR>\n" );
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document.write( "Now let's find the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F9%29x-5%2F9 ALIGN=MIDDLE  ALT=\"y=%282%2F9%29x-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which goes through (6,-13)\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=2%2F9 ALIGN=MIDDLE  ALT=\"2%2F9\"   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%282%2F9%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%282%2F9%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%289%2F2%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%289%2F2%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=-9%2F2 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-9%2F2\"   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=-9%2F2 ALIGN=MIDDLE  ALT=\"-9%2F2\"   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=-9%2F2 ALIGN=MIDDLE  ALT=\"-9%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%2F9 ALIGN=MIDDLE  ALT=\"2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F9%29%2Ax-5%2F9 ALIGN=MIDDLE  ALT=\"y=%282%2F9%29%2Ax-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (6,-13), 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%2B13=%28-9%2F2%29%2A%28x-6%29 ALIGN=MIDDLE  ALT=\"y%2B13=%28-9%2F2%29%2A%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-9%2F2 ALIGN=MIDDLE  ALT=\"m=-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=6 ALIGN=MIDDLE  ALT=\"x%5B1%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-13 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-13\"   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%2B13=%28-9%2F2%29%2Ax%2B%289%2F2%29%286%29 ALIGN=MIDDLE  ALT=\"y%2B13=%28-9%2F2%29%2Ax%2B%289%2F2%29%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2F2 ALIGN=MIDDLE  ALT=\"-9%2F2\"   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%2B13=%28-9%2F2%29%2Ax%2B54%2F2 ALIGN=MIDDLE  ALT=\"y%2B13=%28-9%2F2%29%2Ax%2B54%2F2\"   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=%28-9%2F2%29%2Ax%2B54%2F2-13 ALIGN=MIDDLE  ALT=\"y=%28-9%2F2%29%2Ax%2B54%2F2-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13 ALIGN=MIDDLE  ALT=\"-13\"   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=%28-9%2F2%29%2Ax%2B54%2F2-26%2F2 ALIGN=MIDDLE  ALT=\"y=%28-9%2F2%29%2Ax%2B54%2F2-26%2F2\"   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=%28-9%2F2%29%2Ax%2B28%2F2 ALIGN=MIDDLE  ALT=\"y=%28-9%2F2%29%2Ax%2B28%2F2\"   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=%28-9%2F2%29%2Ax%2B14 ALIGN=MIDDLE  ALT=\"y=%28-9%2F2%29%2Ax%2B14\"   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=%282%2F9%29%2Ax-5%2F9 ALIGN=MIDDLE  ALT=\"y=%282%2F9%29%2Ax-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13 ALIGN=MIDDLE  ALT=\"-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-9%2F2%29%2Ax%2B14 ALIGN=MIDDLE  ALT=\"y=%28-9%2F2%29%2Ax%2B14\"   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=%282%2F9%29%2Ax-5%2F9 ALIGN=MIDDLE  ALT=\"y=%282%2F9%29%2Ax-5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-9%2F2%29%2Ax%2B14 ALIGN=MIDDLE  ALT=\"y=%28-9%2F2%29%2Ax%2B14\"   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%2C11%2C-18%2C0%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-5%2C11%2C-18%2C0%2C+0.222222222222222%2Ax%2B-5%2F9%2C+-4.5%2Ax%2B14%29%2C%0D%0A+++++++++++circle%286%2C-13%2C0.05%29%2C%0D%0A+++++++++++circle%286%2C-13%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=%282%2F9%29%2Ax-5%2F9 ALIGN=MIDDLE  ALT=\"y=%282%2F9%29%2Ax-5%2F9\"   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=%28-9%2F2%29%2Ax%2B14 ALIGN=MIDDLE  ALT=\"y=%28-9%2F2%29%2Ax%2B14\"   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=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13 ALIGN=MIDDLE  ALT=\"-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<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%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   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%2F3%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%281%2F3%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%283%2F1%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%283%2F1%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=-3%2F1 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-3%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=-3 ALIGN=MIDDLE  ALT=\"-3\"   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=-3 ALIGN=MIDDLE  ALT=\"-3\"   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%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2Ax%2B2 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (-3,1), 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-1=-3%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y-1=-3%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=-3 ALIGN=MIDDLE  ALT=\"m=-3\"   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=1 ALIGN=MIDDLE  ALT=\"y%5B1%5D=1\"   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-1=-3%2Ax%2B%283%29%28-3%29 ALIGN=MIDDLE  ALT=\"y-1=-3%2Ax%2B%283%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   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-1=-3%2Ax-9 ALIGN=MIDDLE  ALT=\"y-1=-3%2Ax-9\"   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=-3%2Ax-9%2B1 ALIGN=MIDDLE  ALT=\"y=-3%2Ax-9%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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=-3%2Ax-8 ALIGN=MIDDLE  ALT=\"y=-3%2Ax-8\"   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=%281%2F3%29%2Ax%2B2 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax%2B2\"   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=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2Ax-8 ALIGN=MIDDLE  ALT=\"y=-3%2Ax-8\"   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=%281%2F3%29%2Ax%2B2 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2Ax-8 ALIGN=MIDDLE  ALT=\"y=-3%2Ax-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=drawing%28+500%2C+500%2C+-8%2C5%2C-4%2C7%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-8%2C5%2C-4%2C7%2C+0.333333333333333%2Ax%2B2%2C+-3%2Ax%2B-8%29%2C%0D%0A+++++++++++circle%28-3%2C1%2C0.05%29%2C%0D%0A+++++++++++circle%28-3%2C1%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=%281%2F3%29%2Ax%2B2 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax%2B2\"   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=-3%2Ax-8 ALIGN=MIDDLE  ALT=\"y=-3%2Ax-8\"   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=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "#3\r<BR>\n" );
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document.write( "First convert the standard equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=3 ALIGN=MIDDLE  ALT=\"x%2B3y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into slope intercept form\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=converting_linear_equations.solver>Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B3y=3 ALIGN=MIDDLE  ALT=\"1x%2B3y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B3y-1x=3-1x ALIGN=MIDDLE  ALT=\"1x%2B3y-1x=3-1x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1x from both sides<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-1x%2B3 ALIGN=MIDDLE  ALT=\"3y=-1x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283y%29%2F%283%29=%28-1x%2B3%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%283y%29%2F%283%29=%28-1x%2B3%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to isolate y<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1x%29%2F%283%29%2B%283%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y+=+%28-1x%29%2F%283%29%2B%283%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction on the right hand side<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F3%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce and simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B3y=3 ALIGN=MIDDLE  ALT=\"1x%2B3y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F3%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F3%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <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;\" > is the slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y intercept.<br><br><br></TD></TR>\n" );
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document.write( "Now let's find the equation of the line that is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which goes through (6,-1)\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%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   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%28-1%2F3%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%28-1%2F3%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%283%2F-1%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%283%2F-1%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=3%2F1 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=3%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=3 ALIGN=MIDDLE  ALT=\"3\"   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=3 ALIGN=MIDDLE  ALT=\"3\"   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%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F3%29%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (6,-1), 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%2B1=3%2A%28x-6%29 ALIGN=MIDDLE  ALT=\"y%2B1=3%2A%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=6 ALIGN=MIDDLE  ALT=\"x%5B1%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-1\"   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%2B1=3%2Ax-%283%29%286%29 ALIGN=MIDDLE  ALT=\"y%2B1=3%2Ax-%283%29%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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%2B1=3%2Ax-18 ALIGN=MIDDLE  ALT=\"y%2B1=3%2Ax-18\"   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=3%2Ax-18-1 ALIGN=MIDDLE  ALT=\"y=3%2Ax-18-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   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=3%2Ax-19 ALIGN=MIDDLE  ALT=\"y=3%2Ax-19\"   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=%28-1%2F3%29%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-19 ALIGN=MIDDLE  ALT=\"y=3%2Ax-19\"   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=%28-1%2F3%29%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-19 ALIGN=MIDDLE  ALT=\"y=3%2Ax-19\"   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%2C11%2C-6%2C6%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-5%2C11%2C-6%2C6%2C+-0.333333333333333%2Ax%2B1%2C+3%2Ax%2B-19%29%2C%0D%0A+++++++++++circle%286%2C-1%2C0.05%29%2C%0D%0A+++++++++++circle%286%2C-1%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=%28-1%2F3%29%2Ax%2B1 ALIGN=MIDDLE  ALT=\"y=%28-1%2F3%29%2Ax%2B1\"   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=3%2Ax-19 ALIGN=MIDDLE  ALT=\"y=3%2Ax-19\"   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=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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