document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161513>Question 161513</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh>ELEMENTARY AND INTERMEDIATE ALGEBRA</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A 10-ounce soft drink sells for 50 cents, and a 16-ounce<BR>\n" );
document.write( "soft drink sells for 68 cents. The price P is determined<BR>\n" );
document.write( "from the volume v of the cup by a linear equation.<BR>\n" );
document.write( "a) Find the equation.<BR>\n" );
document.write( "b) Find the price of a 20-ounce soft drink. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118988 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = ounces<BR>\n" );
document.write( "y = price<BR>\n" );
document.write( "slope intercept form of the equation is<BR>\n" );
document.write( "y = m*x + b<BR>\n" );
document.write( "you need 2 point on the graph to find the slope.<BR>\n" );
document.write( "one of the points is (10,50)<BR>\n" );
document.write( "the other point is (16,68)<BR>\n" );
document.write( "slope is determined by the formula<BR>\n" );
document.write( "(y-y1)/(x-x1)<BR>\n" );
document.write( "let (x,y) = (16,68)<BR>\n" );
document.write( "let (x1,y1) = (10,50)<BR>\n" );
document.write( "slope is then<BR>\n" );
document.write( "(68-50)/(16-10) = 18/6 = 3<BR>\n" );
document.write( "slope intercept form of the equation becomes<BR>\n" );
document.write( "y = 3*x + b<BR>\n" );
document.write( "to solve for b, use one of the points.<BR>\n" );
document.write( "take (x1,y1) = (10,50)<BR>\n" );
document.write( "equation becomes<BR>\n" );
document.write( "50 = 3*(10) + b<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "50 = 30 + b<BR>\n" );
document.write( "subtract 30 from both sides of equation to get<BR>\n" );
document.write( "50 - 30 = b<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "20 = b<BR>\n" );
document.write( "slope intercept form of the equation is now<BR>\n" );
document.write( "y = 3*x + 20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove this is good, substitute the known points in the equation.<BR>\n" );
document.write( "first use (10,50)<BR>\n" );
document.write( "equation becomes<BR>\n" );
document.write( "50 = 3*(10) + 20<BR>\n" );
document.write( "50 = 30 + 20<BR>\n" );
document.write( "50 = 50<BR>\n" );
document.write( "equation is good for first set of points.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "next use (16,68)<BR>\n" );
document.write( "equation becomes<BR>\n" );
document.write( "68 = 3*(16) + 20<BR>\n" );
document.write( "68 = 48 + 20<BR>\n" );
document.write( "68 = 68<BR>\n" );
document.write( "equation is good for the second set of points.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equation is<BR>\n" );
document.write( "y = 3*x + 20<BR>\n" );
document.write( "use the equation to solve for when x = 20.<BR>\n" );
document.write( "substitute 20 for x and the equation becomes<BR>\n" );
document.write( "y = 3*(20) + 20<BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "y = 60 + 20<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "y = 80<BR>\n" );
document.write( "price for a 20 ounce soda would be 80 cents.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "graph of the equation should show that when x = 20, y = 80<BR>\n" );
document.write( "graph of the equation is shown below.<BR>\n" );
document.write( "x axis represents ounces of soda.<BR>\n" );
document.write( "y axis represents cost of soda in cents.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28800%2C800%2C-10%2C30%2C-10%2C100%2C3%2Ax%2B20%29 ALIGN=MIDDLE  ALT=\"graph+%28800%2C800%2C-10%2C30%2C-10%2C100%2C3%2Ax%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );