document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204541>Question 204541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (3) When graphing a linear inequality, how do you know if the inequality represents the area above the line? Give examples.<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 #154408 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you follow the inequality.<BR>\n" );
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document.write( "assume y < x<BR>\n" );
document.write( "you graph y = x.<BR>\n" );
document.write( "the area under the graph of the equation  y = x is the area you are interested in.<BR>\n" );
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document.write( "assume y < -x<BR>\n" );
document.write( "you graph y = -x<BR>\n" );
document.write( "the area under the graph of the equation y = -x is the area you are interested in.<BR>\n" );
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document.write( "you have two equations or constraints.<BR>\n" );
document.write( "y < x<BR>\n" );
document.write( "y < -x<BR>\n" );
document.write( "these are 2 intersecting lines that are perpendicular to each other.<BR>\n" );
document.write( "you graph y = x<BR>\n" );
document.write( "you graph y = -x<BR>\n" );
document.write( "the area under the graph of the equation y = x and the graph of the equation y = -x is the area you are interested in.<BR>\n" );
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document.write( "suppose you have 3 equations or constraints.<BR>\n" );
document.write( "y < x<BR>\n" );
document.write( "y < -x<BR>\n" );
document.write( "y > -3<BR>\n" );
document.write( "you graph y = x<BR>\n" );
document.write( "you graph y = -x<BR>\n" );
document.write( "you graph y = -3<BR>\n" );
document.write( "the area you are interested is the area under the graph of the equation y = x and the area under the graph of the equation y = -x and the area above the graph of the equation y = -3<BR>\n" );
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document.write( "a graph of the 3 equations would look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%2C-x%2C-3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%2C-x%2C-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you can see on this graph that if you were only concerned with y < x, then any value of y under the graph of the equation y = x would be good.<BR>\n" );
document.write( "if x = -4, then y < -4 would satisfy the inequality.<BR>\n" );
document.write( "if x = 4, then y < 4 would satisfy the inequality.<BR>\n" );
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document.write( "you can see on this graph that if you were only concerned with y < -x, then any value of y under the graph of the equation y = -x would be good.<BR>\n" );
document.write( "if x = -4, then y < 4 would satisfy the inequality<BR>\n" );
document.write( "if x = 4, then y < -4 would satisfy the inequality.<BR>\n" );
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document.write( "you can see on this graph that if you were concerned with y < x and y < -x, then any value of y under the graph of the equation y = x and under the graph of the equation y = -x would be good.<BR>\n" );
document.write( "if x = -4, then y would have to be smaller than -4<BR>\n" );
document.write( "if x = 4, then y would have to be smaller than -4 again.<BR>\n" );
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document.write( "you can see on this graph that if you were concerned with y < x and y < -x and y > -3, then any value of y under the graph of the equation y = x and under the graph of the equation y = -x and above the graph of y = -3 would be good.<BR>\n" );
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document.write( "if x = -4, then there would be no y values that would satisfy the inequality because y could not be below -4 and above -3 at the same time.<BR>\n" );
document.write( "if x = 4, then there would be no y values that would satisfy the inequality because y could not be below -4 again and above -3 at the same time.<BR>\n" );
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document.write( "x would have to be between -3 and 3 and then y would have to be below the lines y = -x and y = x and above the line y = -3.<BR>\n" );
document.write( "if x was 2, then y would have to be below -2 and above -3. <BR>\n" );
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document.write( "to spot the area where you want to be sometimes it's necessary to take some points to verify what you are seeing is what satisfies all equations in the inequality.<BR>\n" );
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document.write( "if the inequality is <, than the area of interest is below the graph of the equation.<BR>\n" );
document.write( "if the inequality is >, than the area of interest is above the graph of the equation.<BR>\n" );
document.write( "the graph of the equation is the equality.<BR>\n" );
document.write( "example:<BR>\n" );
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document.write( "y = x^2 + 3x + 5 is the equality that is used to graph this equation.<BR>\n" );
document.write( "y < x^2 + 3x + 5 is the area under the graph of this equation.<BR>\n" );
document.write( "y > x^2 + 3x + 5 is the area above the graph of this equation.<BR>\n" );
document.write( "the graph looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+3x+%2B+5%2C3%2C1000000%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+3x+%2B+5%2C3%2C1000000%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "pick any x value on this graph.<BR>\n" );
document.write( "try (-2)<BR>\n" );
document.write( "(-2)^2 + 3*(-2) + 5 = 4 - 6 + 5 = 3<BR>\n" );
document.write( "when x = -2, y = 3 should be on the graph of the equation.<BR>\n" );
document.write( "It is as shown by the intersection of the vertical line at x = -2 and the horizontal line at y = 3.<BR>\n" );
document.write( "when y > 3 you can see it's in the area of the graph above the equation.<BR>\n" );
document.write( "when y < 3 you can see it's in the area of the graph below the equation.<BR>\n" );
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