document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7792>Question 7792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation for a line that passes through (6,8) and is perpendicular to 9x+5y=94? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4294 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=4294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> They give you the line 9x + 5y = 94, right? If you want to find the slope of the line perpendicular to the line given to you, you must first find the slope of the line given to you.\r<BR>\n" );
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document.write( "9x + 5y = 94 needs some work. We need to change that around until we get it to say \"y = \".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x+%2B+5y+=+94+ ALIGN=MIDDLE  ALT=\"+9x+%2B+5y+=+94+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- start here\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5y+=+94+-+9x+ ALIGN=MIDDLE  ALT=\"+5y+=+94+-+9x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- subtracted 9x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+94%2F5+-+%289%2F5%29x+ ALIGN=MIDDLE  ALT=\"+y+=+94%2F5+-+%289%2F5%29x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- divide both sides by 5 so that the y can be alone finally. The -9/5 would be the slope of the line given to you.\r<BR>\n" );
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document.write( "Now, the slope of the perpendicular is ALWAYS the negative (or opposite) reciprocal. If your slope is -9/5, then the opposite reciprocal will be 5/9. What you do is to flip the fraction and change the sign.\r<BR>\n" );
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document.write( "Now, we know that the slope of the perpendicular line will be 5/9. They're given us some additional information. The perpendicular line passes through the point (6,8). There is a formula that exists that we can plug in the slope and a point. That would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28y+-+y%5B0%5D%29+=+m%28x+-+x%5B0%5D%29+ ALIGN=MIDDLE  ALT=\"+%28y+-+y%5B0%5D%29+=+m%28x+-+x%5B0%5D%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where m is your slope, and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D ALIGN=MIDDLE  ALT=\"x%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D ALIGN=MIDDLE  ALT=\"y%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is a given point that the line goes through. Let's plug the values in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28y+-+8%29+=+%285%2F9%29%28x+-+6%29+ ALIGN=MIDDLE  ALT=\"+%28y+-+8%29+=+%285%2F9%29%28x+-+6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- now this needs some work so that we can put it in standard form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%28y+-+8%29+=+5%28x+-+6%29+ ALIGN=MIDDLE  ALT=\"+9%28y+-+8%29+=+5%28x+-+6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- multiply the whole equation by 9 to get rid of the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9y+-+72+=+5x+-+30+ ALIGN=MIDDLE  ALT=\"+9y+-+72+=+5x+-+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- used distributive property.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5x+%2B+9y+=+42+ ALIGN=MIDDLE  ALT=\"+-5x+%2B+9y+=+42+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- moved the 5x to the left (as it became -5x) and added 72 to both sides. This is now our equation in standard form. This is the equation of the line perpendicular to 9x+5y=94. </SPAN>\n" );
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