document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999698>Question 999698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company that makes nails finds that it would sell 42 boxes of nails per month if they are priced at $20 per box. If the company lowers the price to $10 per box, then more people would purchase nails and the company could expect to sell 52 boxes per month. Find the equation of the line for the demand equation if x represents the number of boxes sold and y is the price of a box of nails. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617413 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=617413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> at 20 dollars a box, 42 boxes are sold per month.<BR>\n" );
document.write( "at 10 dollars a box, 52 boxes are sold per mmnth.\r<BR>\n" );
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document.write( "your demand equation is y = mx + b\r<BR>\n" );
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document.write( "y is the price per box.<BR>\n" );
document.write( "x is the demand.<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept\r<BR>\n" );
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document.write( "there are 2 points on your demand line.<BR>\n" );
document.write( "they are (x1,y1) = (42,20) and (x2,y2) = (52,10).\r<BR>\n" );
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document.write( "m = slope = (y2-y1) / (x2-x1) = (10-20)/(52-42) = -10/10 = -1\r<BR>\n" );
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document.write( "y = mx + b becomes:\r<BR>\n" );
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document.write( "y = -1*x + b which becomes:\r<BR>\n" );
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document.write( "y =  -x + b\r<BR>\n" );
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document.write( "to find b, replace x and y with the coordinates of one of the points on the line and solve.\r<BR>\n" );
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document.write( "we'll use (42,20)\r<BR>\n" );
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document.write( "y = -x + b becomes:\r<BR>\n" );
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document.write( "20 = -(42) + b\r<BR>\n" );
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document.write( "add 42 to both sides to get:\r<BR>\n" );
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document.write( "62 = b\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "y = -x + 62\r<BR>\n" );
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document.write( "that's your demand equation.\r<BR>\n" );
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document.write( "when x = 0, y = 62<BR>\n" );
document.write( "when x = 42, y = 20<BR>\n" );
document.write( "when x = 52, y = 0<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "the graph of this equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/102906.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "actually i would call this the price equation because your x value is the demand and your y value is the price.\r<BR>\n" );
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document.write( "since y is dependent on the value of x, that means that price is dependent on the value of the demand.\r<BR>\n" );
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document.write( "you would normally use this equation to find the price given the demand.\r<BR>\n" );
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document.write( "a true demand equation would have x = price and y = demand.\r<BR>\n" );
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document.write( "you would use that equation to find the demand given the price.\r<BR>\n" );
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document.write( "but, the problem stated x = demand and y = price so that's what i created the equation for.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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