document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102866>Question 102866</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131467735/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find B so that -6x +By = 3 is perpendicular to 2x-3y=8.\r<BR>\n" );
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document.write( "I took simplified y=-2/3x - 8/3   and y=6x + 3/B.  <BR>\n" );
document.write( "any number for B must be positive in order for the lines to be perpendicular.\r<BR>\n" );
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document.write( "is this correct? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74808 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=74808\">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=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-3y=8 ALIGN=MIDDLE  ALT=\"2x-3y=8\"   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-3y-2x=8-2x ALIGN=MIDDLE  ALT=\"2x-3y-2x=8-2x\"   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=-3y=-2x%2B8 ALIGN=MIDDLE  ALT=\"-3y=-2x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3y%29%2F%28-3%29=%28-2x%2B8%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"%28-3y%29%2F%28-3%29=%28-2x%2B8%29%2F%28-3%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+=+%28-2x%29%2F%28-3%29%2B%288%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2x%29%2F%28-3%29%2B%288%29%2F%28-3%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%2F3%29x-8%2F3 ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x-8%2F3\"   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-3y=8 ALIGN=MIDDLE  ALT=\"2x-3y=8\"   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%2F3%29x-8%2F3 ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x-8%2F3\"   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%2F3%29x-8%2F3 ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x-8%2F3\"   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%2F3 ALIGN=MIDDLE  ALT=\"m=2%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=-8%2F3 ALIGN=MIDDLE  ALT=\"b=-8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y intercept.<br><br><br></TD></TR>\n" );
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document.write( "So this means the perpendicular slope is 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;\" >. So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x+%2BBy+=+3 ALIGN=MIDDLE  ALT=\"-6x+%2BBy+=+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=-6x%2BBy=3 ALIGN=MIDDLE  ALT=\"-6x%2BBy=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=By=3%2B6x ALIGN=MIDDLE  ALT=\"By=3%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 6x to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2B6x%29%2FB ALIGN=MIDDLE  ALT=\"y=%283%2B6x%29%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2FB%2B%286%2FB%29x ALIGN=MIDDLE  ALT=\"y=3%2FB%2B%286%2FB%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >Break up the fraction\r<BR>\n" );
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document.write( "So the slope of this equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2FB ALIGN=MIDDLE  ALT=\"6%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in order to be perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=8 ALIGN=MIDDLE  ALT=\"2x-3y=8\"   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=6%2FB=-3%2F2 ALIGN=MIDDLE  ALT=\"6%2FB=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2FB ALIGN=MIDDLE  ALT=\"6%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   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=6=%28-3%2F2%29%2AB ALIGN=MIDDLE  ALT=\"6=%28-3%2F2%29%2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A2=-3%2AB ALIGN=MIDDLE  ALT=\"6%2A2=-3%2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=-3%2AB ALIGN=MIDDLE  ALT=\"12=-3%2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F-3=B ALIGN=MIDDLE  ALT=\"12%2F-3=B\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=B ALIGN=MIDDLE  ALT=\"-4=B\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-4 ALIGN=MIDDLE  ALT=\"B=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So B is equal to -4 in order to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x+%2BBy+=+3 ALIGN=MIDDLE  ALT=\"-6x+%2BBy+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=8 ALIGN=MIDDLE  ALT=\"2x-3y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, the equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x+-4y+=+3 ALIGN=MIDDLE  ALT=\"-6x+-4y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=8 ALIGN=MIDDLE  ALT=\"2x-3y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice I replaced B with -4) </SPAN>\n" );
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