document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122430>Question 122430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a 2-day rental, a rental car agency charges a $40 fee per day plus $0.35 per mile. <BR>\n" );
document.write( "  The equation   represents this model, where C symbolizes the total cost of <BR>\n" );
document.write( "  the rental, and x stands for the number of miles driven.   \r<BR>\n" );
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document.write( "A. Find the y-intercept of this graph and explain what it means in the context of the problem. Show all work to receive full credit. <BR>\n" );
document.write( "B. Explain the slope of the line within the context of this problem. <BR>\n" );
document.write( "C. Graph the equation. <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 #90044 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=90044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem establishes that you are going to rent a car for 2 days. <BR>\n" );
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document.write( "Ask yourself how you would compute the cost of that rental. The problem tells you that you<BR>\n" );
document.write( "will pay $40 per day, and this means that for a two-day rental you will pay $80. <BR>\n" );
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document.write( "But you will also have to pay $0.35 per mile for each mile that you drive. If you drive zero<BR>\n" );
document.write( "miles you will have to pay the $80. However, if you drive 10 miles, you will not only have<BR>\n" );
document.write( "to pay the $80, you will also have to pay $0.35 times 10 which equals $3.50. So your total<BR>\n" );
document.write( "cost for the two-day rental with 10 miles driven is $80 + $3.50 = $83.50<BR>\n" );
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document.write( "What if you drive 100 miles over the two days. You would owe the rental company $80 plus<BR>\n" );
document.write( "$0.35 times 100 which is $35.00. So your total bill would be $115.00 for the two days.<BR>\n" );
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document.write( "If you establish that your graph has the number of miles driven as the horizontal <BR>\n" );
document.write( "axis and the total cost of the rental as the vertical axis, you then have three points you can <BR>\n" );
document.write( "plot. Those points are (0,80) and (10, 83.50) and (100, 115). These are the points that<BR>\n" );
document.write( "you figured out above. <BR>\n" );
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document.write( "The form of the equation we can write to describe this graph is the slope-intercept<BR>\n" );
document.write( "form. The slope-intercept form is (in this case C is the y-axis value):<BR>\n" );
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document.write( "C = mx + b<BR>\n" );
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document.write( "where m is the slope of the graph and b is the value on the vertical axis where the graph<BR>\n" );
document.write( "crosses the vertical axis.  <BR>\n" );
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document.write( "For your problem b is the fixed cost of $80. When x equals 0 miles, b the cost was $80<BR>\n" );
document.write( "so the intercept on the Cost (or vertical axis) is $80. <BR>\n" );
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document.write( "The slope, m, is 0.35 because each time x gets bigger by 1 unit, the Cost goes up by $0.35 units.<BR>\n" );
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document.write( "So the cost equation that you are graphing is:<BR>\n" );
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document.write( "C = 0.35x + 80<BR>\n" );
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document.write( "If you just plug in the value of x (which is the number of miles driven) you get the total<BR>\n" );
document.write( "cost of the rental ... or C. Drive 500 miles and the cost is:<BR>\n" );
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document.write( "C = 0.35*500 + 80 = 175 + 80 = 255<BR>\n" );
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document.write( "So for a two day rental with 500 miles driven, the cost would be $255 and on the graph this<BR>\n" );
document.write( "would plot as the point (500, 255).<BR>\n" );
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document.write( "Your graph should look something like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-60%2C1000%2C-20%2C400%2C+0.35x%2B80%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-60%2C1000%2C-20%2C400%2C+0.35x%2B80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that it crosses the vertical axis at +80. And the slope is 0.35. When you graph it,<BR>\n" );
document.write( "you will want to choose some better values along the x-axis and y-axis ... not all the <BR>\n" );
document.write( "\"un-nice\" values shown on the above graph. Maybe make the x-axis in terms like 100, 200, 300, and so<BR>\n" );
document.write( "on, and the y-axis (for Cost) in terms of 50, 100, 150, 200, and so on. Something that<BR>\n" );
document.write( "is a little easier to read than the graph shown above.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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