document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123847>Question 123847</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0130519669/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do I graph inequalities with two variable so that I will know what direction to shade solutions?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90850 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=90850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Example: <BR>\n" );
document.write( "3x - 4y < 2<BR>\n" );
document.write( "1st: solve for \"y\":<BR>\n" );
document.write( "y >= (3/4)x - (1/2)<BR>\n" );
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document.write( "2nd: Graph the boundary which is y = (3/4)x-(1/2)<BR>\n" );
document.write( "Graph this line as a dashed line because \"equality\" was not part of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%283%2F4%29x-%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%283%2F4%29x-%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "3rd: Select a test point that is not on the boundary, like (0,0)<BR>\n" );
document.write( "4th: Check to see if this point satisfied the INEQUALITY y>(3/4)x-(1/2)<BR>\n" );
document.write( "You get: 0 > (3/4)*0-(1/2) ; 0>-1/2<BR>\n" );
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document.write( "Conclusion: That is true so the half-plane solution for the Inequality is on <BR>\n" );
document.write( "the same side of the boundary as the point (0,0).<BR>\n" );
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document.write( "If the result had been false, the half-plane solution would be <BR>\n" );
document.write( "on the side that does not contain (0,0)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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