document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123320>Question 123320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the line passing through the two points. show that this line is perpendicular to the given line.\r<BR>\n" );
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document.write( "(4,2) and (-4,6); y=2x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90501 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=90501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equation of the point passing through 2 points is given by: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+y1%29%2F%28y2+-+y1%29 ALIGN=MIDDLE  ALT=\"%28y+-+y1%29%2F%28y2+-+y1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+x1%29%2F%28x2+-+x1%29+ ALIGN=MIDDLE  ALT=\"%28x+-+x1%29%2F%28x2+-+x1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The two points are: (4, 2) and (-4, 6) \r<BR>\n" );
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document.write( "plugging in these points: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+2%29%2F%286+-+2%29 ALIGN=MIDDLE  ALT=\"%28y+-+2%29%2F%286+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+4%29%2F%28-4+-+4%29 ALIGN=MIDDLE  ALT=\"%28x+-+4%29%2F%28-4+-+4%29\"   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=%28y+-+2%29%2F4+ ALIGN=MIDDLE  ALT=\"%28y+-+2%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+4%29%2F%28-8%29 ALIGN=MIDDLE  ALT=\"%28x+-+4%29%2F%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> (y - 2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+4%29%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"%28x+-+4%29%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "This can be written as: \r<BR>\n" );
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document.write( "==> 2(y - 2) = (-)(x - 4)\r<BR>\n" );
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document.write( "==> 2y - 4 = -x + 4 \r<BR>\n" );
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document.write( "==> 2y + x - 4 - 4 = 0\r<BR>\n" );
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document.write( "==> 2y + x - 8 = 0 \r<BR>\n" );
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document.write( "Or ==> y = -x/2 + 4 -------------------(1)\r<BR>\n" );
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document.write( "This is the equation of the line. \r<BR>\n" );
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document.write( "So now to check whether the above equation is perpendicular to the given line \r<BR>\n" );
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document.write( "y = 2x + 3   --------------------------(2)\r<BR>\n" );
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document.write( "For thsi condition to satisfy the product of their slopes should be equal to negative 1.\r<BR>\n" );
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document.write( "So first lets find the slope of eqn (1) ==> m1 = -1/2 \r<BR>\n" );
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document.write( "Slope of eqn (2) ==> m2 = 2 \r<BR>\n" );
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document.write( "So now the product of m1 & m2 = (-1/2) * (2)  = -1 \r<BR>\n" );
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document.write( "Hence both the lines are penpendicular. \r<BR>\n" );
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document.write( "Regards\r<BR>\n" );
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document.write( " </SPAN>\n" );
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