document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134196>Question 134196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the inequality: y < (1/2)x + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98132 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=98132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F2%29x+%2B+1 ALIGN=MIDDLE  ALT=\"y+=+%281%2F2%29x+%2B+1\"   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=+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%281%2F2%29x%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%281%2F2%29x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x+%2B+1 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B2y%3C2 ALIGN=MIDDLE  ALT=\"-x%2B2y%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the test point\r<BR>\n" );
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document.write( "Substitute (0,0) into the inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C%281%2F2%29%280%29+%2B+1 ALIGN=MIDDLE  ALT=\"0%3C%281%2F2%29%280%29+%2B+1\"   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%3C1 ALIGN=MIDDLE  ALT=\"0%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of <a  rel=nofollow HREF=http://www.mozilla.com/en-US/firefox/>Firefox</a> to see these images.)\r<BR>\n" );
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document.write( "Since this inequality is true, we simply shade the entire region that contains (0,0)\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%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-3%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-9%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-15%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-21%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-27%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-30%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-33%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-39%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-42%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%2B-45%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F2%29x%2B1%2C%281%2F2%29x%2B1%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%281%2F2%29x+%2B+1 ALIGN=MIDDLE  ALT=\"y%3C%281%2F2%29x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the boundary (which is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x+%2B+1 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in red) and the shaded region (in green) <BR>\n" );
document.write( "(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)<BR>\n" );
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