document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549972>Question 549972</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. Determine graphically the co-ordinates of the vertices of a triangle, the equation of whose sides are given:<BR>\n" );
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document.write( "(i) y = x ; y = 2x ; x + y = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358291 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=358291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To graph a line, all you have to do is determine two points, plot them, and connect them.<BR>\n" );
document.write( "Line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x=0 ALIGN=MIDDLE  ALT=\"y=x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving us the point (0,0).<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x=6 ALIGN=MIDDLE  ALT=\"y=x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving us the point (6,6).<BR>\n" );
document.write( "Line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x ALIGN=MIDDLE  ALT=\"y=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x=0 ALIGN=MIDDLE  ALT=\"y=2x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving us the point (0,0).<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x=2%2A3=6 ALIGN=MIDDLE  ALT=\"y=2x=2%2A3=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving us the point (3,6).<BR>\n" );
document.write( "Line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+=+6 ALIGN=MIDDLE  ALT=\"+x+%2B+y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y=0%2By=y=6 ALIGN=MIDDLE  ALT=\"x+%2B+y=0%2By=y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving us the point (0,6).<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y=x%2B0=x=6 ALIGN=MIDDLE  ALT=\"x+%2B+y=x%2B0=x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving us the point (6,0).<BR>\n" );
document.write( "Plotting all 3 pairs of points, and connecting each pair to make the corresponding line, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C7%2C-1%2C7%2C%0D%0Agrid%281%29%2Cline%28-1%2C-1%2C7%2C7%29%2Cline%28-1%2F2%2C-1%2C3.5%2C7%29%2Cline%28-1%2C7%2C7%2C-1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The vertices appear to be (0,0), (2,4), and (3,3).<BR>\n" );
document.write( "We know that (0,0) is a point in the first two lines (we used that point to graph them).<BR>\n" );
document.write( "We should verify that (2,4) and (3,3) are indeed at the intersection of line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=6 ALIGN=MIDDLE  ALT=\"x%2By=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the first two lines, but that is so mental-math obvious that I'm going to skip it and proclaim that the three vertices are indeed (0,0), (2,4), and (3,3). </SPAN>\n" );
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