document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132398>Question 132398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, again I need some help this paper is due tomorrow hope someone has time to help. I need to create a function using this information.<BR>\n" );
document.write( "year  Median Home Cost<BR>\n" );
document.write( "1989   $93,100<BR>\n" );
document.write( "1990   $97,500<BR>\n" );
document.write( "1991   $99,700<BR>\n" );
document.write( "1992   $100,900<BR>\n" );
document.write( "1993   $106,100<BR>\n" );
document.write( "Using the data from 1989 and 1992 determine the values for M and B and then create a linear functionf(x) = mx + b.<BR>\n" );
document.write( "m_____; B_____ f(x) = __________.\r<BR>\n" );
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document.write( "Thanks for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96741 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=96741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you need to use all the data that is given, then use your calculator to calculate the linear regression. \r<BR>\n" );
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document.write( "If you just want to find the line through the points (1989, 93100) and (1992,100900) then let's make the year 1989 as x=0 (ie we're starting at the year 1989)\r<BR>\n" );
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document.write( "So the two points then become (0, 93100) and (3,100900). Notice how 1992 is 3 years from 1989. So at 1992, we have x=3\r<BR>\n" );
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document.write( "Now let's find the equation of the line through the points (0, 93100) and (3,100900)\r<BR>\n" );
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document.write( "First lets find the slope through the points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93100 ALIGN=MIDDLE  ALT=\"93100\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100900 ALIGN=MIDDLE  ALT=\"100900\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the slope formula (note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_{1},y_{1}\right)\"> is the first point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93100 ALIGN=MIDDLE  ALT=\"93100\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_{2},y_{2}\right)\"> is the second point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100900 ALIGN=MIDDLE  ALT=\"100900\"   DISABLED_style= \"max-width:90%; height:auto;\" >))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28100900-93100%29%2F%283-0%29 ALIGN=MIDDLE  ALT=\"m=%28100900-93100%29%2F%283-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=100900 ALIGN=MIDDLE  ALT=\"y%5B2%5D=100900\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=93100 ALIGN=MIDDLE  ALT=\"y%5B1%5D=93100\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=3 ALIGN=MIDDLE  ALT=\"x%5B2%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=0 ALIGN=MIDDLE  ALT=\"x%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (these are the coordinates of given points)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=+7800%2F3 ALIGN=MIDDLE  ALT=\"m=+7800%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100900-93100 ALIGN=MIDDLE  ALT=\"100900-93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7800 ALIGN=MIDDLE  ALT=\"7800\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Subtract the terms in the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-0 ALIGN=MIDDLE  ALT=\"3-0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2600 ALIGN=MIDDLE  ALT=\"m=2600\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the slope is\r<BR>\n" );
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document.write( "Now let's use the point-slope formula to find the equation of the line:\r<BR>\n" );
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document.write( "------Point-Slope Formula------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(\textrm{x_{1},y_{1}}\right)\"> is one of the given points\r<BR>\n" );
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document.write( "So lets use the Point-Slope Formula to find the equation of the line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-93100=%282600%29%28x-0%29 ALIGN=MIDDLE  ALT=\"y-93100=%282600%29%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2600 ALIGN=MIDDLE  ALT=\"m=2600\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=0 ALIGN=MIDDLE  ALT=\"x%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=93100 ALIGN=MIDDLE  ALT=\"y%5B1%5D=93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values are given)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-93100=2600x%2B%282600%29%280%29 ALIGN=MIDDLE  ALT=\"y-93100=2600x%2B%282600%29%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2600 ALIGN=MIDDLE  ALT=\"2600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-93100=2600x%2B0 ALIGN=MIDDLE  ALT=\"y-93100=2600x%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2600 ALIGN=MIDDLE  ALT=\"2600\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2600x%2B0%2B93100 ALIGN=MIDDLE  ALT=\"y=2600x%2B0%2B93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93100 ALIGN=MIDDLE  ALT=\"93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to  both sides to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2600x%2B93100 ALIGN=MIDDLE  ALT=\"y=2600x%2B93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93100 ALIGN=MIDDLE  ALT=\"93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93100 ALIGN=MIDDLE  ALT=\"93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the equation of the line which goes through the points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93100 ALIGN=MIDDLE  ALT=\"93100\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100900 ALIGN=MIDDLE  ALT=\"100900\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  is:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2600x%2B93100 ALIGN=MIDDLE  ALT=\"y=2600x%2B93100\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (or in function notation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2600x%2B93100 ALIGN=MIDDLE  ALT=\"f%28x%29=2600x%2B93100\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
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document.write( "The equation is now in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > form (which is slope-intercept form) where the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2600 ALIGN=MIDDLE  ALT=\"m=2600\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=93100 ALIGN=MIDDLE  ALT=\"b=93100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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