document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934305>Question 934305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jason wants to buy rose plants and sunflower plants for his garden. Rose plants cost $10 each, and sunflower plants cost $15 each and his spending limit is $300. The inequality 10x+15y is equal to or greater than 300 models the total amount of money Jason can spend on plants, where x represents the number of rose plants and y represents the number of sunflowers plants. Graph the inequality. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568725 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=568725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is 10x + 15y <= 300\r<BR>\n" );
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document.write( "this is because the total that he spends has to be less than or equal to 300.\r<BR>\n" );
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document.write( "to graph this inequality, you would graph the equality and then look for the area on the graph that represents the inequality.\r<BR>\n" );
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document.write( "the equation you graph would be:\r<BR>\n" );
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document.write( "10x + 15y = 300\r<BR>\n" );
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document.write( "to graph it, solve for y to get:\r<BR>\n" );
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document.write( "y = (300 - 10x) / 15\r<BR>\n" );
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document.write( "you can simplify this, and you can put it in slope intercept form, but it's not necessary.\r<BR>\n" );
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document.write( "it will graph the same either way.\r<BR>\n" );
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document.write( "i'll convert it for you so you can see how it works.\r<BR>\n" );
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document.write( "start with y = (300 - 10x) / 15\r<BR>\n" );
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document.write( "distribute the division to get:\r<BR>\n" );
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document.write( "y = 300 / 15 - 10x / 15\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "y = 20 - 2/3 * x\r<BR>\n" );
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document.write( "re-order the terms to get:\r<BR>\n" );
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document.write( "y = - 2/3 * x + 20\r<BR>\n" );
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document.write( "- 2/3 is the slope<BR>\n" );
document.write( "20 is the y intercept.\r<BR>\n" );
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document.write( "to manually graph it, you pick 2 values of x and solve for y and then draw a straight line between them.\r<BR>\n" );
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document.write( "to use graphing software, you merely enter the equation into the graphing software and it will show you the graph, assuming you have set the scale of the x and y axis correctly.\r<BR>\n" );
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document.write( "the graph of that equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C40%2C-10%2C30%2C-2%2F3+%2A+x+%2B+20%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C40%2C-10%2C30%2C-2%2F3+%2A+x+%2B+20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "once you graph it, you look for the area that satisfies the inequality.\r<BR>\n" );
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document.write( "the area on that graph that satisfies the inequality is all points on the graph that are below the line y = -2/3 * x + 20,\r<BR>\n" );
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document.write( "you would shade that area to show you that it is the area on the grpah that satisfies the inequality.\r<BR>\n" );
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document.write( "if it's hard to see, you simply find one value of x that is on the graph and then look for a value of y that is below that.\r<BR>\n" );
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document.write( "for example, when x = 15, y will be equal to -2/3 * 20 + 20 which will be equal to -10 + 20 which will be equal to 10.\r<BR>\n" );
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document.write( "the coordinate point on the line when x = 15 will be (15,10).\r<BR>\n" );
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document.write( "i drew a horizontal line on the graph at y = 10.  look at the intersection of that horizontal line with the graph of the equation and then look vertically down from there and you will see that x = 15 at that point.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C40%2C-10%2C30%2C-2%2F3+%2A+x+%2B+20%2C+10%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C40%2C-10%2C30%2C-2%2F3+%2A+x+%2B+20%2C+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when x = 15, any value of y less than 10 will be below the line and any value of y greater than 10 will be above the line.\r<BR>\n" );
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document.write( "since you are looking for all values of y smaller than or equal to 10, than any value of y less than 10 will satisfy the inequality portion of the equation and will be below the line.\r<BR>\n" );
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document.write( "you can do the same analysis for any other point on the line.<BR>\n" );
document.write( "evaluate the equality portion of the equation at any other point on the line to find the value of y that will be on the line at that value of x.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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