document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310701>Question 310701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When graphing, how do I know if the line should be solid or broken, and also what part should i shade? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222188 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=222188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If your inequality symbol is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large >\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large <\"> then use a broken line for the boundary.  This means that points on the line are NOT included in the solution set.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If your inequality symbol is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \geq\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \leq\"> then use a solid line for the boundary. This means that points on the line ARE included in the solution set.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once you have the boundary line graphed, pick any point you like that is NOT ON THE LINE.  If the line does not pass through the origin, the origin itself is a very good selection for a test point.  Otherwise, pick something with small integer coefficients -- all this so that the arithmetic is easier.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute the coordinates of the point you chose into the original inequality.  If the result is a true statement, shade in the side of the line that CONTAINS the point you chose.  If the result is a false statement, shade in the side of the line that DOES NOT CONTAIN the point you chose.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -3x\ +\ y\ \leq\ 2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This doesn't go through the origin so, lets try (0,0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -3(0)\ +\ (0)\ \leq^?\ 2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Yep, zero is less than 2, so the shading happens on the side of the line containing the origin.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=plot_any_inequality.solver>Plot Any Inequality</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Graphing function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=3x%2B2 ALIGN=MIDDLE  ALT=\"y%3C=3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=3x%2B2+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=3x%2B2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );