document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271635>Question 271635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Social Security benefits. If you earned an average of<BR>\n" );
document.write( "$25,000 over your working life and you retire after 2005 at<BR>\n" );
document.write( "age 62, 63, or 64, then your annual Social Security benefit<BR>\n" );
document.write( "will be $7000, $7500, or $8000, respectively (Social<BR>\n" );
document.write( "Security Administration, www.ssa.gov). There is a linear<BR>\n" );
document.write( "equation that gives the annual benefit b in terms of age a for<BR>\n" );
document.write( "these three years. Find the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198907 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=198907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your point pairs are (x,y) = :\r<BR>\n" );
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document.write( "62,7000<BR>\n" );
document.write( "63,7500<BR>\n" );
document.write( "64,8000\r<BR>\n" );
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document.write( "the slope of the equation will be:\r<BR>\n" );
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document.write( "(8000 - 7000) / (64 - 62)\r<BR>\n" );
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document.write( "this becomes 1000 / 2 = 500\r<BR>\n" );
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document.write( "the equation will be y = 500 * x + b\r<BR>\n" );
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document.write( "take one of the points and replace x and y with it.\r<BR>\n" );
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document.write( "take the 63,7500 pair.\r<BR>\n" );
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document.write( "the slope intercept form of the equation becomes:\r<BR>\n" );
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document.write( "7500 = 500*63 + b which becomes:\r<BR>\n" );
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document.write( "7500 = 31500 + b\r<BR>\n" );
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document.write( "subtract 31500 from both sides of this equation to get:\r<BR>\n" );
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document.write( "b = -24000\r<BR>\n" );
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document.write( "that's the y-intercept of the equation which is the value of y when x = 0\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "y = 500x - 24000\r<BR>\n" );
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document.write( "a graph of your 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%2C100%2C-30000%2C30000%2C500x+-+24000%29 ALIGN=MIDDLE  ALT=\"graph+%28600%2C600%2C-10%2C100%2C-30000%2C30000%2C500x+-+24000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a closer view of the graph to show the years of interest better 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+%281200%2C300%2C-10%2C70%2C-1000%2C10000%2C500x+-+24000%2C7000%2C7500%2C8000%29 ALIGN=MIDDLE  ALT=\"graph+%281200%2C300%2C-10%2C70%2C-1000%2C10000%2C500x+-+24000%2C7000%2C7500%2C8000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that y = 7000 when x = 62 and y = 7500 when x - 63 and y = 8000 when x = 64.\r<BR>\n" );
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document.write( "the 3 horizontal lines are at y = 7000, 7500, 8000 respectively.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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