document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169601>Question 1169601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> England. Like everything else, the ticket prices to Six Flags continue to increase every year.  Because of this, your family is planning to buy a family membership this year that includes reduced admission costs, discounts on food and drinks, free parking and “skip the line” passes every time you visit.\r<BR>\n" );
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document.write( "Your parents have asked you to determine which membership plan would be best for your family.   The table below summarizes the three membership options: \r<BR>\n" );
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document.write( "O1 Gold membership: $225 per visit\r<BR>\n" );
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document.write( "O2 Platinum Membership: Original payment of $750 plus $100 every visit.\r<BR>\n" );
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document.write( "O3 Diamond Membership: You pay an initial membership fee of $1575. On your first visit you pay $25, on your second visit you pay $50 and on your third visit you pay $75. This constant rate of change applies to every visit you make.\r<BR>\n" );
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document.write( "Let C represent the cost function and let v represent the number of visits to Six Flags you make during the summer months. Write a linear function in slope intercept form for each membership option. Is there a y-intercept for each option?  What is the rate of change for each option?  Use the variables identified in the word problem to write the equations.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851311 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely, let's analyze the Six Flags membership options and create linear functions for each.\r<BR>\n" );
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document.write( "**Understanding the Problem**\r<BR>\n" );
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document.write( "We need to create linear functions (in slope-intercept form, y = mx + b) for the cost of each membership option based on the number of visits. We also need to identify the y-intercept and the rate of change for each option.\r<BR>\n" );
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document.write( "**Variables**\r<BR>\n" );
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document.write( "* C: Total cost<BR>\n" );
document.write( "* v: Number of visits\r<BR>\n" );
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document.write( "**Membership Options**\r<BR>\n" );
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document.write( "* **O1 Gold Membership:**<BR>\n" );
document.write( "    * Cost: $225 per visit<BR>\n" );
document.write( "    * Equation: C = 225v<BR>\n" );
document.write( "    * Y-intercept: 0 (no initial fee)<BR>\n" );
document.write( "    * Rate of change: 225 (cost increases by $225 per visit)\r<BR>\n" );
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document.write( "* **O2 Platinum Membership:**<BR>\n" );
document.write( "    * Cost: $750 initial payment + $100 per visit<BR>\n" );
document.write( "    * Equation: C = 100v + 750<BR>\n" );
document.write( "    * Y-intercept: 750 (initial payment of $750)<BR>\n" );
document.write( "    * Rate of change: 100 (cost increases by $100 per visit)\r<BR>\n" );
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document.write( "* **O3 Diamond Membership:**<BR>\n" );
document.write( "    * Cost: $1575 initial payment + $25 for the first visit, $50 for the second visit, $75 for the third visit, etc.<BR>\n" );
document.write( "    * This indicates that the cost per visit increases by $25 for each subsequent visit.<BR>\n" );
document.write( "    * To find the general equation, we need to find the cost per visit for the \"v\"th visit.<BR>\n" );
document.write( "    * The cost for the \"v\"th visit will be 25 * v.<BR>\n" );
document.write( "    * Therefore the total cost is.<BR>\n" );
document.write( "    * Equation: C = 1575 + 25v<BR>\n" );
document.write( "    * Y-intercept: 1575 (initial payment of $1575)<BR>\n" );
document.write( "    * Rate of change: 25 (cost increases by $25 per visit)\r<BR>\n" );
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document.write( "**Summary**\r<BR>\n" );
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document.write( "* **O1 Gold:** C = 225v<BR>\n" );
document.write( "    * Y-intercept: 0<BR>\n" );
document.write( "    * Rate of change: 225<BR>\n" );
document.write( "* **O2 Platinum:** C = 100v + 750<BR>\n" );
document.write( "    * Y-intercept: 750<BR>\n" );
document.write( "    * Rate of change: 100<BR>\n" );
document.write( "* **O3 Diamond:** C = 25v + 1575<BR>\n" );
document.write( "    * Y-intercept: 1575<BR>\n" );
document.write( "    * Rate of change: 25<BR>\n" );
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