document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189034>Question 1189034</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.  Another line L4 is parallel to L1  and passes through (-1,3) find the x and y- intercepts L4  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820255 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=820255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two equations are:\r<BR>\n" );
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document.write( "2y - 3x - 6 = 0 = L1<BR>\n" );
document.write( "3y + x + 20 = 0 = L2\r<BR>\n" );
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document.write( "third equation is the line parallel to 2y - 3x - 6 = 0 and passing through the point (-1,3).\r<BR>\n" );
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document.write( "if parallel, it has the same slope as L1.\r<BR>\n" );
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document.write( "the slope intercept form of L1 is calculated below:\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 L1.<BR>\n" );
document.write( "L4 will have the same slope, so L4 equation will be:<BR>\n" );
document.write( "y = 3/2 * x + b<BR>\n" );
document.write( "b is the y-intercept.<BR>\n" );
document.write( "since L4 passes through the point (-1,3), then replace y with 3 and x with -1 to get:<BR>\n" );
document.write( "3 = 3/2 * -1 + b<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "3 = -3/2 + b<BR>\n" );
document.write( "add 3/2 to both sides to get:<BR>\n" );
document.write( "3 + 3/2 = b<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "9/2 = b\r<BR>\n" );
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document.write( "the equation of L4 parallel to L1 is y = 3/2 * x Z+ 9/2\r<BR>\n" );
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document.write( "the graph of L1 and L4 is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/122101.jpg\" >\r<BR>\n" );
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document.write( "the blue line is L4.<BR>\n" );
document.write( "you can see that the line passes through the point (-1,3).<BR>\n" );
document.write( "can also see that the vertical separation between the red line and the blue line is always 1.5 units.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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