document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165387>Question 165387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is my problem and I believe I have the answer (C(x))=3x+27,000 but I don't know the proper process for illustrating this.  Please help!\r<BR>\n" );
document.write( "\n" );
document.write( "# If the relationship between the total cost and the number of units produced is linear and if the total cost increases by $3 for each additional unit made:\r<BR>\n" );
document.write( "\n" );
document.write( "   1. Find the equation of the total cost function C(x) using the fact that  C(1,000) = 30,000 (dollars) where x is the number of units produced.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121890 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=121890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the \"total cost increases by $3 for each additional unit made\", this means that the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, because C(1,000) = 30,000 , this means that we have the point (1000,30000).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's find the equation of the line that has a slope of 3 and goes through the point (1000,30000)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you want to find the equation of line with a given a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which goes through the point (1000,30000), you can simply use the point-slope formula to find the equation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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(x_{1},y_{1}\right)\"> is the given point\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So lets use the Point-Slope Formula to find the equation of the line\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-30000=%283%29%28x-1000%29 ALIGN=MIDDLE  ALT=\"y-30000=%283%29%28x-1000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=1000 ALIGN=MIDDLE  ALT=\"x%5B1%5D=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=30000 ALIGN=MIDDLE  ALT=\"y%5B1%5D=30000\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values are given)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-30000=3x%2B%283%29%28-1000%29 ALIGN=MIDDLE  ALT=\"y-30000=3x%2B%283%29%28-1000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-30000=3x-3000 ALIGN=MIDDLE  ALT=\"y-30000=3x-3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1000 ALIGN=MIDDLE  ALT=\"-1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3000 ALIGN=MIDDLE  ALT=\"-3000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-3000%2B30000 ALIGN=MIDDLE  ALT=\"y=3x-3000%2B30000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 30000 to  both sides to isolate y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B27000 ALIGN=MIDDLE  ALT=\"y=3x%2B27000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3000 ALIGN=MIDDLE  ALT=\"-3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30000 ALIGN=MIDDLE  ALT=\"30000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27000 ALIGN=MIDDLE  ALT=\"27000\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the equation of the line with a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which goes through the point (1000,30000) is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B27000 ALIGN=MIDDLE  ALT=\"y=3x%2B27000\"   DISABLED_style= \"max-width:90%; height:auto;\" > which 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 where the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   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=27000 ALIGN=MIDDLE  ALT=\"b=27000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So in function notation, the cost function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=3x%2B27000 ALIGN=MIDDLE  ALT=\"C%28x%29=3x%2B27000\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So you are correct.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );