document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162780>Question 1162780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturing company finds that they can sell 450 items at $2.00 per item and 225 items at $3.50 per item. If the relationship between the number of items sold x and the price per item p is a linear one:\r<BR>\n" );
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document.write( "Find a formula that gives x in terms of p: x= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786632 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=786632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you want a linear relationship between x and p<BR>\n" );
document.write( "that would be a straight line equation with the general form of y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept<BR>\n" );
document.write( "since you x in terms of p, then:<BR>\n" );
document.write( "let y = x<BR>\n" );
document.write( "let x = p<BR>\n" );
document.write( "the equation of y = mx + b is the same as the equation of x = mp + b after you replace y with x and x with p.<BR>\n" );
document.write( "in the equation of x = mp + b, you have coordinate points in the form of (p,x)<BR>\n" );
document.write( "since y = x and x = p, this is the same as the form of (x,y), which is the standard form of the linear equation coordinate points.<BR>\n" );
document.write( "we'll work with x = mp + b and then later translate to y = mx + b for graphing purposes.<BR>\n" );
document.write( "your standard form is x = mp + b with coordinate points of (p,x).<BR>\n" );
document.write( "you have two coordinate points.<BR>\n" );
document.write( "they are (2,450) and (3.5,225)<BR>\n" );
document.write( "m is equal to slope which is equal to (y2-y1)/(x2-x1) which is then translated to (x2-x1)/p2-p1 when you replace y with x and x with p.<BR>\n" );
document.write( "assign (2,450) to (p1,x1) and assign (3.5,225) to (p2,x2) and the slope equation becomes (225-450)/(3.5-2) which becomes -225/1.5 = -150.<BR>\n" );
document.write( "your slope is -150 and your equation of x = mp + b becomes x = -150 * p + b<BR>\n" );
document.write( "replace x and p with one of the points to solve for b.<BR>\n" );
document.write( "i used (2,450).<BR>\n" );
document.write( "the equation of x = mp + b becomes 450 = -150 * 2 + b<BR>\n" );
document.write( "solve for b to get b = 750.<BR>\n" );
document.write( "the equation becomes x = -150 * p + 750.<BR>\n" );
document.write( "that's your final equation.<BR>\n" );
document.write( "to graph it, i replaced x ith y and p with x to get y = -150 * x + 750.<BR>\n" );
document.write( "the graph is shown below.\r<BR>\n" );
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document.write( "the equation of y = -150 * x + 750 is for graphing purposes only.\r<BR>\n" );
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document.write( "your solution is the equation of x = -150 * p + 750\r<BR>\n" );
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document.write( "x represents the number of items sold.<BR>\n" );
document.write( "p represents the price of each item.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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