document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118012>Question 118012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of each line. Give the answer in standard formusing only integers as the coefficients.\r<BR>\n" );
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document.write( "The line through (2,-3) that is perpendicular to the line y=-3x+12<BR>\n" );
document.write( "The answer is x-3y=11<BR>\n" );
document.write( "How do I work the problem to find the answer given? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86054 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=86054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\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 ALIGN=MIDDLE  ALT=\"-3\"   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%2F1%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=-1%2F%28-3%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%29 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=%28-1%2F1%29%281%2F-3%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=1%2F3 ALIGN=MIDDLE  ALT=\"m%5Bp%5D=1%2F3\"   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=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   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=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   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 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2Ax%2B12 ALIGN=MIDDLE  ALT=\"y=-3%2Ax%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\n" );
document.write( "Also since the unknown line goes through (2,-3), 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%2B3=%281%2F3%29%2A%28x-2%29 ALIGN=MIDDLE  ALT=\"y%2B3=%281%2F3%29%2A%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-3 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-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%2B3=%281%2F3%29%2Ax-%281%2F3%29%282%29 ALIGN=MIDDLE  ALT=\"y%2B3=%281%2F3%29%2Ax-%281%2F3%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <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;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3=%281%2F3%29%2Ax-2%2F3 ALIGN=MIDDLE  ALT=\"y%2B3=%281%2F3%29%2Ax-2%2F3\"   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=%281%2F3%29%2Ax-2%2F3-3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-2%2F3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   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=%281%2F3%29%2Ax-2%2F3-9%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-2%2F3-9%2F3\"   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=%281%2F3%29%2Ax-11%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-11%2F3\"   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=%281%2F3%29%2Ax-11%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-11%2F3\"   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%2Ax%2B12 ALIGN=MIDDLE  ALT=\"y=-3%2Ax%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and goes through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2Ax-11%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-11%2F3\"   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%2Ax%2B12 ALIGN=MIDDLE  ALT=\"y=-3%2Ax%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29%2Ax-11%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-11%2F3\"   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%2C7%2C-8%2C17%2C+%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++graph%28+500%2C+500%2C+-5%2C7%2C-8%2C17%2C+-3%2Ax%2B12%2C+0.333333333333333%2Ax%2B-3.66666666666667%29%2C%0D%0A+++++++++++circle%282%2C-3%2C0.05%29%2C%0D%0A+++++++++++circle%282%2C-3%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%2Ax%2B12 ALIGN=MIDDLE  ALT=\"y=-3%2Ax%2B12\"   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=%281%2F3%29%2Ax-11%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29%2Ax-11%2F3\"   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=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<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( "Now let's convert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x-11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to standard 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 slope-intercept form (y = mx+b) to standard form (Ax+By = C)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"y+=+%281%2F3%29x-11%2F3\"   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=3%2Ay+=+3%2A%28%281%2F3%29x-11%2F3%29 ALIGN=MIDDLE  ALT=\"3%2Ay+=+3%2A%28%281%2F3%29x-11%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 3<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+1x-11 ALIGN=MIDDLE  ALT=\"3y+=+1x-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-1x+=+1x-11-1x ALIGN=MIDDLE  ALT=\"3y-1x+=+1x-11-1x\"   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=-1x%2B3y+=+-11 ALIGN=MIDDLE  ALT=\"-1x%2B3y+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28-1x%2B3y%29+=+-1%2A%28-11%29 ALIGN=MIDDLE  ALT=\"-1%2A%28-1x%2B3y%29+=+-1%2A%28-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by -1 to make the A coefficient positive (note: this step may be optional; it will depend on your teacher and/or textbook)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x-3y+=+11 ALIGN=MIDDLE  ALT=\"1x-3y+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"y+=+%281%2F3%29x-11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x-3y+=+11 ALIGN=MIDDLE  ALT=\"1x-3y+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form where A > 0)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x-3y+=+11 ALIGN=MIDDLE  ALT=\"1x-3y+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%2BBy+=+C ALIGN=MIDDLE  ALT=\"Ax%2BBy+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+1 ALIGN=MIDDLE  ALT=\"A+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+-3 ALIGN=MIDDLE  ALT=\"B+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+11 ALIGN=MIDDLE  ALT=\"C+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br><br></TD></TR>\n" );
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document.write( "Since the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3y=11 ALIGN=MIDDLE  ALT=\"x-3y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, I'm assuming that the book wants A to be positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%28-x%2B3y%29=%28-1%29%28-11%29 ALIGN=MIDDLE  ALT=\"-1%28-x%2B3y%29=%28-1%29%28-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B3y=-11 ALIGN=MIDDLE  ALT=\"-x%2B3y=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > by -1 \r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3y=11 ALIGN=MIDDLE  ALT=\"x-3y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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