document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202086>Question 202086</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780077224820/algebrahomeworkh>Elementary and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The equation S= 5000 + 200x and D=9500 -100x express suppy S and demand D, respectively, for a popular compact disc in terms of its price x (in dollars).<BR>\n" );
document.write( "Graph the equations on the same coordinate system.<BR>\n" );
document.write( "What happens to the supply as the price increases?<BR>\n" );
document.write( "What happens to the demand as the price increases?<BR>\n" );
document.write( "What is the equilibrium price?<BR>\n" );
document.write( " Please show your work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152887 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=152887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you move the x terms in front of the constant terms in both equations, you end up with the Slope-intercept form (y = mx + b) of the equation of a line:<BR>\n" );
document.write( "S = 200x + 5000<BR>\n" );
document.write( "which tells us the slope, m, is 200 and the y-intercept is 5000 (or the point (0, 5000).<BR>\n" );
document.write( "D = -100x + 9500<BR>\n" );
document.write( "which tells us the slope is -100 and the y-intercept is 9500. With this information you should be able to graph these lines. (A graph is provided below.)<br><BR>\n" );
document.write( "From the slope of supply equation (or by looking at the graph of the supply equation) we can tell what happens to the supply as the price goes up. Since the slope is positive, as one value (the price) goes up the other value (supply) also goes up.<br><BR>\n" );
document.write( "Similarly the slope of the demand equation is negative. So as the price goes up, the demand will go down.<br><BR>\n" );
document.write( "The equilibrium point is where the supply equals the demand. Graphically this is the point where the lines intersect. Algebraically we can use the fact that if D = S then 200x + 5000 = -100x + 9500. We can solve this equaltion:<BR>\n" );
document.write( "Add 100x to both sides:<BR>\n" );
document.write( "300x + 5000 = 9500<BR>\n" );
document.write( "Subtract 5000 from both sides:<BR>\n" );
document.write( "300x = 4500<BR>\n" );
document.write( "Divide both sides by 300:<BR>\n" );
document.write( "x = 15<BR>\n" );
document.write( "This tells us that the equilibrium point is where x = 15. We can find the supply (and demand since they are the same at the equilibrium point) by substituting 15 for x in either the supply or demand equation:<BR>\n" );
document.write( "S = 200(15) + 5000<BR>\n" );
document.write( "S = 3000 + 5000<BR>\n" );
document.write( "S = 8000<BR>\n" );
document.write( "The equilibrium point is (15, 8000).<br><BR>\n" );
document.write( "The graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C+600%2C+-2%2C+22%2C+0%2C+10000%2C+200x+%2B+5000%2C+-100x+%2B+9500%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C+600%2C+-2%2C+22%2C+0%2C+10000%2C+200x+%2B+5000%2C+-100x+%2B+9500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );