document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145489>Question 145489</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534463878/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> graph the inequality y<3x+1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106143 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=106143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C3x%2B1 ALIGN=MIDDLE  ALT=\"y%3C3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the 1st inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B1 ALIGN=MIDDLE  ALT=\"y=3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace the inequality sign with an equals sign\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=y%3C3x%2B1 ALIGN=MIDDLE  ALT=\"y%3C3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to plot the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B1 ALIGN=MIDDLE  ALT=\"y=3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > first\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%2C3x%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B1 ALIGN=MIDDLE  ALT=\"y=3x%2B1\"   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%3C3x%2B1 ALIGN=MIDDLE  ALT=\"y%3C3x%2B1\"   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%3C3%2A%280%29%2B1 ALIGN=MIDDLE  ALT=\"0%3C3%2A%280%29%2B1\"   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;\" > 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). So this means that we shade everything <b>below</b> the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B1 ALIGN=MIDDLE  ALT=\"y=3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: Since the inequality is a \"less than\" sign, this means that the line should be a dotted 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+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-0%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-2%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-4%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-8%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-10%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-14%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-16%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-20%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-22%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-26%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-28%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-30%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C3x%2B1%2C3x%2B1-32%29%0D%0A%0D%0A+%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%3C3x%2B1 ALIGN=MIDDLE  ALT=\"y%3C3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in green\r<BR>\n" );
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