document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120206>Question 120206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the standard form of the line that passes through (5,-3) and has a slope perpendicular to 2x+7y=16. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88093 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First step is to find the required slope value.  Perpendicular lines have slopes that are negative reciprocals of each other:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-%281%2Fm%5B2%5D%29 ALIGN=MIDDLE  ALT=\"m%5B1%5D=-%281%2Fm%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The equation of the perpendicular is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B7y=16 ALIGN=MIDDLE  ALT=\"2x%2B7y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Put this into slope-intercept 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;\" >, by solving for y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B7y=16 ALIGN=MIDDLE  ALT=\"2x%2B7y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y=-2x%2B16 ALIGN=MIDDLE  ALT=\"7y=-2x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28-2%29%2F7%29x+%2B16 ALIGN=MIDDLE  ALT=\"y=%28%28-2%29%2F7%29x+%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which tells us that the slope of the perpendicular to the desired line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F7%29 ALIGN=MIDDLE  ALT=\"-%282%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-%281%2Fm%5B2%5D%29 ALIGN=MIDDLE  ALT=\"m%5B1%5D=-%281%2Fm%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we now know that the slope of the desired line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now we have a point, (5,-3) and a slope, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so use the point slope form of the line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-y%5B1%5D%29=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y-y%5B1%5D%29=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;\" >) are the coordinates of the given point.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-3%29=%287%2F2%29%28x-5%29%29 ALIGN=MIDDLE  ALT=\"y-%28-3%29=%287%2F2%29%28x-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now simplify to standard form:\r<BR>\n" );
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document.write( "Multiply by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B6=7%28x-5%29 ALIGN=MIDDLE  ALT=\"2y%2B6=7%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B6=7x-35 ALIGN=MIDDLE  ALT=\"2y%2B6=7x-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add -7x to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x%2B2y%2B6=-35 ALIGN=MIDDLE  ALT=\"-7x%2B2y%2B6=-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add -6 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x%2B2y=-41 ALIGN=MIDDLE  ALT=\"-7x%2B2y=-41\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the desired equation, though it would be a little tidier to multiply through by -1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-2y=41 ALIGN=MIDDLE  ALT=\"7x-2y=41\"   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=graph%28600%2C600%2C-20%2C20%2C-20%2C20%2Cgrid%282%29%2C-%282x%2F7%29%2B16%2C%287%2F2%29x-%2841%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope this helps,<BR>\n" );
document.write( "John\r<BR>\n" );
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document.write( " </SPAN>\n" );
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