document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150623>Question 150623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that a market place research company finds that at a price of p =$20, they would sell x=42 tiles each month. If the lower the price to p= $10,then more people would purchase the tile and they can expect to sell x= 52 tiles in a month's time. Find the equation of the line for the demand equation . Write your answer in the form p=mx+b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110558 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=110558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the demand equation (p = mx+b) if p = $20 when x = 42 and p = $10 when x = 52.<BR>\n" );
document.write( "First, you can find the slope, m, of the line represented by this equation.<BR>\n" );
document.write( "p is the dependent variable and x is the independent variable.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28p%5B2%5D-p%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28p%5B2%5D-p%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make the substitutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D+=+20 ALIGN=MIDDLE  ALT=\"p%5B1%5D+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D+=+10 ALIGN=MIDDLE  ALT=\"p%5B2%5D+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+42 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+52 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2810-20%29%2F%2852-42%29 ALIGN=MIDDLE  ALT=\"m+=+%2810-20%29%2F%2852-42%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+=+%28-10%29%2F10 ALIGN=MIDDLE  ALT=\"m+=+%28-10%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-1 ALIGN=MIDDLE  ALT=\"m+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so now you can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-1%29x%2Bb ALIGN=MIDDLE  ALT=\"p+=+%28-1%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > but now you need to find b, the p-intercept. Just substitute the p- and x-values from the given data, but make sure that you match the appropriate p with the right x (in other words, mind your p's and x's...lol).<BR>\n" );
document.write( "Let's use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D+=+20 ALIGN=MIDDLE  ALT=\"p%5B1%5D+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+42 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+=+%28-1%29%2842%29%2Bb ALIGN=MIDDLE  ALT=\"20+=+%28-1%29%2842%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+=+-42%2Bb ALIGN=MIDDLE  ALT=\"20+=+-42%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 42 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=62+=+b ALIGN=MIDDLE  ALT=\"62+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you can write your final equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-x%2B62 ALIGN=MIDDLE  ALT=\"p+=+-x%2B62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-x%2B62 ALIGN=MIDDLE  ALT=\"p+=+-x%2B62\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = 42.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-42%2B62 ALIGN=MIDDLE  ALT=\"p+=+-42%2B62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+20 ALIGN=MIDDLE  ALT=\"p+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-x%2B62 ALIGN=MIDDLE  ALT=\"p+=+-x%2B62\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = 52.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-52%2B62 ALIGN=MIDDLE  ALT=\"p+=+-52%2B62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+10 ALIGN=MIDDLE  ALT=\"p+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK<BR>\n" );
document.write( "Here's the graph of the demand equation: (The vertical axis is p and the horizontal axis is x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C65%2C-5%2C65%2C-x%2B62%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C65%2C-5%2C65%2C-x%2B62%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );