document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=579312>Question 579312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 250 boxes. But when you raise your price to $5 you only sell 120 boxes. \r<BR>\n" );
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document.write( "a.   Write an equation for the number of boxes you sell as a function of the price you charge. \r<BR>\n" );
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document.write( "b.   Denote \"B\" for number of boxes, and \"P\" for the price you charge.\r<BR>\n" );
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document.write( "c.   Assume the function is linear </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #370935 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=370935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the cost per cookie box.<BR>\n" );
document.write( "let y equal the number of cookie boxes you sell.<BR>\n" );
document.write( "you have 2 points that you can use to make a straight line equation.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "(x1,y1) = (3,250)<BR>\n" );
document.write( "(x2,y2) = (5,120)<BR>\n" );
document.write( "these 2 points can be used to generate a straight line equation using the point slope form.<BR>\n" );
document.write( "the point slope form of the equation for a straight line is:<BR>\n" );
document.write( "y - y1 = m * (x - x1)<BR>\n" );
document.write( "it can also be:<BR>\n" );
document.write( "y - y2 = m * (x - x2)<BR>\n" );
document.write( "any point that is on the line can be used.<BR>\n" );
document.write( "m is the slope of the equation.<BR>\n" );
document.write( "the formula to find the slope is:<BR>\n" );
document.write( "m = (y2 - y1) / (x2 - x1)<BR>\n" );
document.write( "you use both points to find the slope.<BR>\n" );
document.write( "substituting for y1 and y2 and x1 and x2, we get:<BR>\n" );
document.write( "m = (120 - 250) / (5 - 3)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "m = -130 / 2 which becomes:<BR>\n" );
document.write( "m = -65<BR>\n" );
document.write( "our slope is -65 and our equation becomes:<BR>\n" );
document.write( "y - y1 = -65 * (x - x1)<BR>\n" );
document.write( "or it becomes:<BR>\n" );
document.write( "y - y2 = -65 * (x - x2)<BR>\n" );
document.write( "we can use either point.<BR>\n" );
document.write( "we'll use (x1,y1) = (3,250)<BR>\n" );
document.write( "when we use that point, our equation becomes:<BR>\n" );
document.write( "y - 250 = -65 * (x - 3)<BR>\n" );
document.write( "we simplify this to get:<BR>\n" );
document.write( "y - 250 = -65x + 195<BR>\n" );
document.write( "add 250 to both sides of this equation to get:<BR>\n" );
document.write( "y = -65x + 195 + 250 which becomes:<BR>\n" );
document.write( "y = -65x + 445<BR>\n" );
document.write( "that's our equation.<BR>\n" );
document.write( "the equation looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-30%2C500%2C-65x%2B445%2C250%2C120%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-30%2C500%2C-65x%2B445%2C250%2C120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see from the graph that when x = 3, y = 250, and when x = 5, y = 120.<BR>\n" );
document.write( "the horizontal lines at y = 250 and y = 120 are there to help you see that.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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