document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67116>Question 67116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Business and finance. In planning for a new item, a manufacturer assumes that<BR>\n" );
document.write( "the number of items produced x and the cost in dollars C of producing these items<BR>\n" );
document.write( "are related by a linear equation. Projections are that 100 items will cost $10,000 to<BR>\n" );
document.write( "produce and that 300 items will cost $22,000 to produce. Find the equation that<BR>\n" );
document.write( "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 #47730 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=47730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Business and finance. In planning for a new item, a manufacturer assumes that<BR>\n" );
document.write( "the number of items produced x and the cost in dollars C of producing these items<BR>\n" );
document.write( "are related by a linear equation. Projections are that 100 items will cost $10,000 to<BR>\n" );
document.write( "produce and that 300 items will cost $22,000 to produce. Find the equation that<BR>\n" );
document.write( "relates C and x.<BR>\n" );
document.write( "You are probably familiar with finding the equations of lines when you're given two points, (x1,y1) and (x2,y2).  If so just change y1 and y2 into C1 and C2.<BR>\n" );
document.write( "(x1,C1)=(100,10000) and (x2,C2)=(300,22000) <BR>\n" );
document.write( "(It would make the numbers easier to deal with if you dealt with C in terms of 1000's and make C1=10 and C2=22.  But I didn't want to confuse you, so I'm going with what you got.  Your teacher may use 10 and 22 and note to the side that C is in terms of thousands.)<BR>\n" );
document.write( "Any way the formula for the slope is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m=%28C2-C1%29%2F%28x2-x1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28m=%28C2-C1%29%2F%28x2-x1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where m=slope and (x1.C1) and (x2,C2) are given points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%2822000-10000%29%2F%28300-100%29 ALIGN=MIDDLE  ALT=\"m=%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=m=12000%2F200 ALIGN=MIDDLE  ALT=\"m=12000%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=60 ALIGN=MIDDLE  ALT=\"m=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that you have a slope, you can use the point-slope formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C-C1=m%28x-x1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28C-C1=m%28x-x1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where m=slope and (x1,C1) is a given point, to find the equation.<BR>\n" );
document.write( "m=60 and (x1,C1)=(100,10000)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C-10000=60%28x-100%29 ALIGN=MIDDLE  ALT=\"C-10000=60%28x-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=C-10000=60x-6000 ALIGN=MIDDLE  ALT=\"C-10000=60x-6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C-10000%2B10000=60x-6000%2B10000 ALIGN=MIDDLE  ALT=\"C-10000%2B10000=60x-6000%2B10000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=60x%2B4000%29 ALIGN=MIDDLE  ALT=\"highlight%28C=60x%2B4000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is another way to do this, if your teacher is using the slope intercept <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;\" >, rather than the point-slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y1=m%28x-x1%29 ALIGN=MIDDLE  ALT=\"y-y1=m%28x-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Let me know and I can show you that way.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );