document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107556>Question 107556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78331 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation is linear, so it will have the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+ax+%2B+b ALIGN=MIDDLE  ALT=\"C+=+ax+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cis plotted on the vertical axis, because it is the <BR>\n" );
document.write( "\"dependant\" variable (dependant on x items produced)<BR>\n" );
document.write( "x is the independant variable plotted on the horizontal axis.<BR>\n" );
document.write( "b is the \"C intercept\". It's the cost of producing zero items<BR>\n" );
document.write( "(overhead). From the points P2(x2,C2) and P1(x1,C1) <BR>\n" );
document.write( " I can determine the slope, a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28C%5B2%5D+-+C%5B1%5D%29+%2F+%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"a+=+%28C%5B2%5D+-+C%5B1%5D%29+%2F+%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B2%5D+=+22000 ALIGN=MIDDLE  ALT=\"C%5B2%5D+=+22000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B1%5D+=+10000 ALIGN=MIDDLE  ALT=\"C%5B1%5D+=+10000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+300 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+100 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%2822000+-+10000%29+%2F+%28300+-+100%29 ALIGN=MIDDLE  ALT=\"a+=+%2822000+-+10000%29+%2F+%28300+-+100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+12000+%2F+200 ALIGN=MIDDLE  ALT=\"a+=+12000+%2F+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+60 ALIGN=MIDDLE  ALT=\"a+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+60x+%2B+b ALIGN=MIDDLE  ALT=\"C+=+60x+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll pick one of the points P(x,C) to solve for b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000+=+60%2A100+%2B+b ALIGN=MIDDLE  ALT=\"10000+=+60%2A100+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+10000+-+6000 ALIGN=MIDDLE  ALT=\"b+=+10000+-+6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+4000 ALIGN=MIDDLE  ALT=\"b+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+60x+%2B+4000 ALIGN=MIDDLE  ALT=\"C+=+60x+%2B+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );