document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=413507>Question 413507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The linear function determines the exchange between the Dollar and the Yen. If in 1990 a dollar was worth 125 yens and in 2010 a dollar is worth 80 yen how many yens will a dollar be worth in 2015 according to this model? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290174 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=290174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in 1990 a dollar was worth 125 yen.<BR>\n" );
document.write( "in 2010 a dollar is worth 80 yen.\r<BR>\n" );
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document.write( "your equation is in the form of y = mx + b where m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "x represents the year<BR>\n" );
document.write( "y represents yen per dollar.\r<BR>\n" );
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document.write( "if we subtract 1990 from the year, then x = 0 represents 1990 and x = 20 represents 2010\r<BR>\n" );
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document.write( "m is the slope.\r<BR>\n" );
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document.write( "x1,y1 = 0,125<BR>\n" );
document.write( "x2,y2 = 20,80\r<BR>\n" );
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document.write( "m is equal to (y2-y1) / (x2-x1) = (80-125) / (20-0) = -45/20 = -9/4\r<BR>\n" );
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document.write( "your equation is now y = (-9/4)x + b\r<BR>\n" );
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document.write( "to find b, substitute either one of the points in the equation and solve for b.\r<BR>\n" );
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document.write( "we'll use x1,y1 = 0,125\r<BR>\n" );
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document.write( "substituting in the equation, we get:\r<BR>\n" );
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document.write( "125 = 0 + b\r<BR>\n" );
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document.write( "this makes b = 125\r<BR>\n" );
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document.write( "your equation now becomes y = (-9/4)x + 125\r<BR>\n" );
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document.write( "in 2015, x will be equal to 2015 - 1990 = 25\r<BR>\n" );
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document.write( "substitute 25 for x in the equation to get:\r<BR>\n" );
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document.write( "y = (-9/4)*25 + 125 = - 56.25 + 125 = 68.75\r<BR>\n" );
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document.write( "in 2015, the dollar will be worth 68.75 yen at the projected straight line rate.\r<BR>\n" );
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document.write( "a graph of this equation is shown below:\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-10%2C30%2C-10%2C130%2C%28-9%2F4%29%2Ax+%2B+125%2C68.75%2C80%2C125%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C30%2C-10%2C130%2C%28-9%2F4%29%2Ax+%2B+125%2C68.75%2C80%2C125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A horizontal line at y = 125 intersects the graph of the equation at x = 0 which is the same as 1990.\r<BR>\n" );
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document.write( "A horizontal line at y = 80 intersects the graph of the equation at x = 20 which is the same as 2010.\r<BR>\n" );
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document.write( "A horizontal line at y = 68.75 intersects the graph of the equation at x = 25 which is the same as 2015.\r<BR>\n" );
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document.write( "The answer is that, in 2015, the dollar will be worth 68.75 yen.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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