document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189033>Question 1189033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two lines L1: 2y-3x-6=0 ad l2: 3y+x-20=0 intersect at a point A. A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y=mx+c  where m and c are constants </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820256 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> L1 equation is 2y - 3x - 6 = 0<BR>\n" );
document.write( "L2 equation is 3y + x  - 20 = 0\r<BR>\n" );
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document.write( "convert both equations to slope intercept form as shown below:\r<BR>\n" );
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document.write( "for L1:\r<BR>\n" );
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document.write( "start with 2y - 3x - 6 = 0<BR>\n" );
document.write( "add 6 to both sides to get 2y - 3x = 6<BR>\n" );
document.write( "add 3x to both sides to get 2y = 3x + 6<BR>\n" );
document.write( "divide both sides by 2 to get y = 3/2 * x + 3\r<BR>\n" );
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document.write( "that's the slope intercept form of the equation for L1.\r<BR>\n" );
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document.write( "for L2:\r<BR>\n" );
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document.write( "start with 3y + x - 20 = 0<BR>\n" );
document.write( "add 20 to both sides to get 3y + x = 20<BR>\n" );
document.write( "subtract x from both sides to get 3y = -x + 20<BR>\n" );
document.write( "divide both sides by 3 to get y = -1/3 * x + 20/3\r<BR>\n" );
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document.write( "that's the slope intercept form of the equation for L2.\r<BR>\n" );
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document.write( "your two equations are:\r<BR>\n" );
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document.write( "L1: y = 3/2 * x + 3<BR>\n" );
document.write( "L2: y = -1/3 * x + 20/3\r<BR>\n" );
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document.write( "solve these two equations simultaneously as shown below:\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:<BR>\n" );
document.write( "0 = 3/2 * x + 1/3 * x + 3 - 20/3<BR>\n" );
document.write( "multiply both sides of the equation by 6 to get:<BR>\n" );
document.write( "0 = 9 * x + 2 * x + 18 - 40<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "0 = 9 * x + 2 * x - 22 <BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "0 = 11 * x - 22<BR>\n" );
document.write( "add 22 to both sides to get:<BR>\n" );
document.write( "22 = 11 * x<BR>\n" );
document.write( "solve for x to get x = 22/11 = 2\r<BR>\n" );
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document.write( "when x = 2, the first eqution of y = 3/2 * x + 3 becomes y = 3/2 * 2 + 3 which b becomes y = 3 + 3 which becomes y = 6.\r<BR>\n" );
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document.write( "the intersection point for L1 and L2 is at (2,6).\r<BR>\n" );
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document.write( "you now want to find L3 perpendicular to L2 and going theough that point.\r<BR>\n" );
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document.write( "the slope intercept form of the equation of L3 will be y = mx + b.<BR>\n" );
document.write( "m is the slope and b is the y-intercept.<BR>\n" );
document.write( "the slope will be the negative reciprocal of the slope of L2.<BR>\n" );
document.write( "the slope of L2 is equal to -1/3.<BR>\n" );
document.write( "the slope of L3 will be 3 because negative reciprocal of -1/3 is 3/1 = 3.<BR>\n" );
document.write( "the equation of L3 becomes y = 3 * x + b<BR>\n" );
document.write( "since it passes through the point (2,6), then replace x with 2 and y with 6 to get:<BR>\n" );
document.write( "6 = 3 * 2 + b<BR>\n" );
document.write( "simplify to get 6 = 6 + b<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = 0<BR>\n" );
document.write( "the equation of L3 is y = 3x<BR>\n" );
document.write( "it is perpendicular to L2 because its slopw is a negative reciprocal of -1/3 and it passes through the point (2,6) which is the intersection point of L1 and L2 and now, L3.\r<BR>\n" );
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document.write( "the graph looks like this.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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