document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103152>Question 103152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How is the meeting point of two linear functions (equations) with differing slopes calculated.\r<BR>\n" );
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document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74999 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Intersection of any two equations (linear or not) is handled by setting the equations equal to each other. <BR>\n" );
document.write( "Here's an example. <BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=m%5B1%5Dx%2Bb%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D=m%5B1%5Dx%2Bb%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=m%5B2%5Dx%2Bb%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D=m%5B2%5Dx%2Bb%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The intersection would be where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D=y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D=y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5Dx%2Bb%5B1%5D=m%5B2%5Dx%2Bb%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5Dx%2Bb%5B1%5D=m%5B2%5Dx%2Bb%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can then proceed to solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5Dx-m%5B2%5Dx%2Bb%5B1%5D=m%5B2%5Dx-m%5B2%5Dx%2Bb%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5Dx-m%5B2%5Dx%2Bb%5B1%5D=m%5B2%5Dx-m%5B2%5Dx%2Bb%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5Dx-m%5B2%5Dx%2Bb%5B1%5D-b%5B1%5D=b%5B2%5D-b%5B1%5D ALIGN=MIDDLE  ALT=\"m%5B1%5Dx-m%5B2%5Dx%2Bb%5B1%5D-b%5B1%5D=b%5B2%5D-b%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5B1%5D-m%5B2%5D%29x=b%5B2%5D-b%5B1%5D ALIGN=MIDDLE  ALT=\"%28m%5B1%5D-m%5B2%5D%29x=b%5B2%5D-b%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bi%5D=%28b%5B2%5D-b%5B1%5D%29%2F%28m%5B1%5D-m%5B2%5D%29 ALIGN=MIDDLE  ALT=\"x%5Bi%5D=%28b%5B2%5D-b%5B1%5D%29%2F%28m%5B1%5D-m%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Once you have x, you can calculate y from (1) or (2) to get your intersection point. <BR>\n" );
document.write( "Here's an example<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B4 ALIGN=MIDDLE  ALT=\"y=2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B5 ALIGN=MIDDLE  ALT=\"y=3x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bi%5D=%285-%284%29%29%2F%282-3%29 ALIGN=MIDDLE  ALT=\"x%5Bi%5D=%285-%284%29%29%2F%282-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bi%5D=-1 ALIGN=MIDDLE  ALT=\"x%5Bi%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bi%5D=2%28-1%29%2B4 ALIGN=MIDDLE  ALT=\"y%5Bi%5D=2%28-1%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bi%5D=2 ALIGN=MIDDLE  ALT=\"y%5Bi%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The intersection point for this example is (-1,2).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+2x%2B4%2C+3x%2B5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+2x%2B4%2C+3x%2B5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Just as an interesting point, if the slopes of your lines were equal to each other, then your equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bi%5D ALIGN=MIDDLE  ALT=\"x%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > would fail because of division by zero<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D-m%5B2%5D=0 ALIGN=MIDDLE  ALT=\"m%5B1%5D-m%5B2%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In that case, since the slopes are equal, the lines never meet because they are parallel.  </SPAN>\n" );
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