document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161643>Question 161643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help please.\r<BR>\n" );
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document.write( "Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $6500 in 1982 and $64,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x).\r<BR>\n" );
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document.write( "a. S(x) = 11,600x + 6,500<BR>\n" );
document.write( "b. S(x) = 58,000x + 64,500<BR>\n" );
document.write( "c. S(x) = 58,000x + 6,500<BR>\n" );
document.write( "d. S(x) = 11,600x + 64,500<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119162 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the years = x and the sales = y<BR>\n" );
document.write( "make x = 0 for 1982.<BR>\n" );
document.write( "then x = 5 for 1987 (1987 - 1982 = 5)<BR>\n" );
document.write( "let y = 6500 for 1982, and y = 64500 for 1987.<BR>\n" );
document.write( "you have two sets of data points.<BR>\n" );
document.write( "they are in the form of (x,y) where x is the x coordinate on the graph and y is the y coordinate on the graph of the equation we're going to create.<BR>\n" );
document.write( "(0,6500)<BR>\n" );
document.write( "(5,64500)<BR>\n" );
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document.write( "line you want to create is given by equation y = m*x + b where m is the slope and b is the y intercept.<BR>\n" );
document.write( "slope is found by taking the change in y and dividing it by the change in x.<BR>\n" );
document.write( "this is given by the formula<BR>\n" );
document.write( "m = (y-y1) / (x-x1)<BR>\n" );
document.write( "let y = 64500 and y1 = 6500<BR>\n" );
document.write( "let x = 5 and x1 = 0<BR>\n" );
document.write( "formula becomes<BR>\n" );
document.write( "m = (64500 - 6500) / (5 - 0) which becomes 58000 / 5 = 11600.<BR>\n" );
document.write( "m = 11600.<BR>\n" );
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document.write( "next you want to find b.<BR>\n" );
document.write( "the equation is y = 11600 * x + b<BR>\n" );
document.write( "substitute one of the known points on the line and solve for b.<BR>\n" );
document.write( "use 5,64500.<BR>\n" );
document.write( "equation becomes<BR>\n" );
document.write( "64500 = 11600 * (5) + b<BR>\n" );
document.write( "64500 = 58000 + b<BR>\n" );
document.write( "b = 64500 - 58000<BR>\n" );
document.write( "b = 6500<BR>\n" );
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document.write( "equation now becomes<BR>\n" );
document.write( "y = 11600 * x + 6500<BR>\n" );
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document.write( "looks like your answer is a.<BR>\n" );
document.write( "to prove, substitute one of the known values in the equation and solve.<BR>\n" );
document.write( "use (0,6500) first<BR>\n" );
document.write( "6500 = 11600 * 0 + 6500 = 6500 <BR>\n" );
document.write( "first one is good.<BR>\n" );
document.write( "use (5,64500) next.<BR>\n" );
document.write( "64500 = 11600 * 5 + 6500 = 58000 + 6500 = 64500<BR>\n" );
document.write( "second one is good.<BR>\n" );
document.write( "answer is a:  y = 11600 * x + 6500<BR>\n" );
document.write( "graph of the equation shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28800%2C800%2C-2%2C10%2C-20000%2C130000%2C11600%2Ax%2B6500%29 ALIGN=MIDDLE  ALT=\"graph+%28800%2C800%2C-2%2C10%2C-20000%2C130000%2C11600%2Ax%2B6500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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