document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106950>Question 1106950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you plot this on a coordinate plane?<BR>\n" );
document.write( "{y=1/2x+4<BR>\n" );
document.write( "{x+4y=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721962 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=721962\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can, and I could tell you how I do it.<BR>\n" );
document.write( "Equation like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y=4 ALIGN=MIDDLE  ALT=\"x%2B4y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "are called linear equations for a good reason:<BR>\n" );
document.write( "their graphs are straight lines.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Two points determine a line,<BR>\n" );
document.write( "so all you need to plot one of those equations<BR>\n" );
document.write( "is to find two pairs of coordinates that satisfy the equation,<BR>\n" );
document.write( "plot them as two points on graph paper,<BR>\n" );
document.write( "and connect the points with a straight line.<BR>\n" );
document.write( "You could find and plot more than two points, but it is not necessary.<BR>\n" );
document.write( "Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x%2B4y=4%29 ALIGN=MIDDLE  ALT=\"red%28x%2B4y=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You realize that when <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=4y=4 ALIGN=MIDDLE  ALT=\"4y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That gives you point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28A%28+0+%2C+1+%29%29 ALIGN=MIDDLE  ALT=\"red%28A%28+0+%2C+1+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Also, when <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=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That gives you point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28B%28+4+%2C+0+%29%29 ALIGN=MIDDLE  ALT=\"red%28B%28+4+%2C+0+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Plotting the points, and connecting them, you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2Cgrid%281%29%2C%0D%0Ared%28circle%280%2C1%2C0.2%29%29%2Cred%28circle%284%2C0%2C0.2%29%29%2C%0D%0Ared%28line%288%2C-1%2C-8%2C3%29%29%2Clocate%284.1%2C0.6%2Cred%28B%29%29%2C%0D%0Alocate%280.1%2C1.6%2Cred%28A%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28y=%281%2F2%29x%2B4%29 ALIGN=MIDDLE  ALT=\"green%28y=%281%2F2%29x%2B4%29\"   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;\" > you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which gives you point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28C%280%2C4%29%29 ALIGN=MIDDLE  ALT=\"green%28C%280%2C4%29%29\"   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=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29%28-4%29%2B4=-2%2B4=-2 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29%28-4%29%2B4=-2%2B4=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That gives you point  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28D%284%2C-2%29%29 ALIGN=MIDDLE  ALT=\"green%28D%284%2C-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Adding those two points, and the line connecting them, you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2Cgrid%281%29%2C%0D%0Ared%28circle%280%2C1%2C0.2%29%29%2Cred%28circle%284%2C0%2C0.2%29%29%2C%0D%0Ared%28line%288%2C-1%2C-8%2C3%29%29%2Clocate%284.1%2C0.6%2Cred%28B%29%29%2C%0D%0Alocate%280.1%2C1.6%2Cred%28A%29%29%2Clocate%280.2%2C4%2Cgreen%28C%29%29%2C%0D%0Agreen%28circle%280%2C4%2C0.2%29%29%2Cgreen%28circle%28-4%2C2%2C0.2%29%29%2C%0D%0Agreen%28line%282%2C5%2C-6%2C1%29%29%2Clocate%28-3.8%2C2%2Cgreen%28D%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The two lines seem to intersect at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28D%28-4%2C2%29%29 ALIGN=MIDDLE  ALT=\"green%28D%28-4%2C2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which happened to be<BR>\n" );
document.write( "a point that we had calculated for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28y=%281%2F2%29x%2B4%29 ALIGN=MIDDLE  ALT=\"green%28y=%281%2F2%29x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That seems to be a solution of the system of linear equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28green%28y=%281%2F2%29x%2B4%29%2Cred%28x%2B4y=4%29%29 ALIGN=MIDDLE  ALT=\"system%28green%28y=%281%2F2%29x%2B4%29%2Cred%28x%2B4y=4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We know that point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28D%28-4%2C2%29%29 ALIGN=MIDDLE  ALT=\"green%28D%28-4%2C2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is part of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28y=%281%2F2%29x%2B4%29 ALIGN=MIDDLE  ALT=\"green%28y=%281%2F2%29x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but we should confirm that it is also part of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x%2B4y=4%29 ALIGN=MIDDLE  ALT=\"red%28x%2B4y=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x%2B4y=4%29 ALIGN=MIDDLE  ALT=\"red%28x%2B4y=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4y=-4=4%282%29=-4%2B8=4 ALIGN=MIDDLE  ALT=\"x%2B4y=-4=4%282%29=-4%2B8=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28D%28-4%2C2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28D%28-4%2C2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x-4%2Cy=2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x-4%2Cy=2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "indeed satisfies both equations,<BR>\n" );
document.write( "meaning that it is the solution for system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28green%28y=%281%2F2%29x%2B4%29%2Cred%28x%2B4y=4%29%29 ALIGN=MIDDLE  ALT=\"system%28green%28y=%281%2F2%29x%2B4%29%2Cred%28x%2B4y=4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );