document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146412>Question 146412</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the inequality on a plane\r<BR>\n" );
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document.write( "4x+5y<=20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106890 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=106890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y%3C=20 ALIGN=MIDDLE  ALT=\"4x%2B5y%3C=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y=20 ALIGN=MIDDLE  ALT=\"4x%2B5y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace the inequality sign with an equals sign.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=20-4x ALIGN=MIDDLE  ALT=\"5y=20-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2820-4x%29%2F%285%29 ALIGN=MIDDLE  ALT=\"y=%2820-4x%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F5%29x%2B4 ALIGN=MIDDLE  ALT=\"y=-%284%2F5%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms and simplify.\r<BR>\n" );
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document.write( "So in order to plot <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5y%3C=20 ALIGN=MIDDLE  ALT=\"4x%2B5y%3C=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-%284%2F5%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3C=-%284%2F5%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is the same thing), we need to plot the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F5%29x%2B20 ALIGN=MIDDLE  ALT=\"y=-%284%2F5%29x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > first. <BR>\n" );
document.write( "(note: if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F5%29x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F5%29x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%284%2F5%29x%2B4 ALIGN=MIDDLE  ALT=\"y=-%284%2F5%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in a test point (0,0) into the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-%284%2F5%29x%2B20 ALIGN=MIDDLE  ALT=\"y%3C=-%284%2F5%29x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-%284%2F5%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3C=-%284%2F5%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=-%284%2F5%29%2A%280%29%2B4 ALIGN=MIDDLE  ALT=\"0%3C=-%284%2F5%29%2A%280%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" > and <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=4 ALIGN=MIDDLE  ALT=\"0%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify.\r<BR>\n" );
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document.write( "Since the inequality is true, this means that we shade the entire region that contains the point (0,0)\r<BR>\n" );
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document.write( "In other words, we simply shade the <b>entire</b> region that is below the line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-48%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-%284%2F5%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3C=-%284%2F5%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in green\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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