document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209122>Question 1209122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me,how do I graph 3x-2y < 6 on a coordinate plane???<BR>\n" );
document.write( "I simplified the equation to: y > 3/2x-3 but I'm not sure if I simplified it correctly.  <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 #847704 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You solved for y correctly.\r<BR>\n" );
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document.write( "Consider the boundary equation y = (3/2)x - 3.\r<BR>\n" );
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document.write( "It's in slope-intercept form y = mx+b<BR>\n" );
document.write( "m = 3/2 = slope<BR>\n" );
document.write( "b = -3 = y intercept\r<BR>\n" );
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document.write( "Start at the anchor point (0,-3) <BR>\n" );
document.write( "This is where the y intercept is located.<BR>\n" );
document.write( "Move 3 units up and 2 units right. This movement pattern is due to the slope.<BR>\n" );
document.write( "You should move from (0,-3) to (2,0)\r<BR>\n" );
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document.write( "Draw a straight line through those points. Extend the line as far as you can in either direction.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-6%2C6%2C-6%2C6%2C-100%2C%283%2F2%29x-3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-6%2C6%2C-6%2C6%2C-100%2C%283%2F2%29x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Make this a dashed line because there isn't an \"or equal to\" in the inequality sign for 3x-2y < 6.<BR>\n" );
document.write( "A dashed line indicates points on the boundary are <u>not</u> in the solution set.\r<BR>\n" );
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document.write( "Now to the question: do we shade above the boundary? or below?<BR>\n" );
document.write( "Since we have something of the form y > mx+b, it means we shade above. <BR>\n" );
document.write( "The greater than symbol tells us this.<BR>\n" );
document.write( "This rule only works if y is fully isolated or when the y coefficient is positive.\r<BR>\n" );
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document.write( "Another way to determine shading direction is to apply a test point like (x,y) = (0,0)<BR>\n" );
document.write( "Make sure the test point is <u>not</u> on the boundary. <BR>\n" );
document.write( "If so then move up or down 1 unit.<BR>\n" );
document.write( "Luckily (0,0) isn't on the boundary.\r<BR>\n" );
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document.write( "Plug the test point into either inequality<BR>\n" );
document.write( "3x-2y < 6<BR>\n" );
document.write( "3*0-2*0 < 6<BR>\n" );
document.write( "0 < 6<BR>\n" );
document.write( "Or,<BR>\n" );
document.write( "y > (3/2)*x - 3<BR>\n" );
document.write( "0 > (3/2)*0 - 3<BR>\n" );
document.write( "0 > -3\r<BR>\n" );
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document.write( "In either case, we get a true statement. <BR>\n" );
document.write( "It proves that (0,0) is in the solution set. <BR>\n" );
document.write( "Therefore, you shade the entire region containing (0,0). <BR>\n" );
document.write( "This is proof we shade above the dashed boundary. \r<BR>\n" );
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document.write( "Graphing tools like <a  rel=nofollow HREF=\"https://www.desmos.com/calculator\">Desmos</a> and <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> are useful to verify the answer.\r<BR>\n" );
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document.write( "Recap:<BR>\n" );
document.write( "Draw a dashed line through the points (0,-3) and (2,0)<BR>\n" );
document.write( "Shade above the dashed line to complete the graph.\r<BR>\n" );
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document.write( "More practice with a similar question found <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1202533.html\">here</a><BR>\n" );
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