document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174272>Question 174272</A>: <I><SPAN STYLE=\"word-break: break-all;\">   <BR>\n" );
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document.write( " Omg, hopefully this is the last one. I do not understand this. Please somebody explain it to me and show me how to do these types of word problems. I greatly appreciate it in advance. <BR>\n" );
document.write( "Say there's a credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.12 . :(\r<BR>\n" );
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document.write( "There is a $23.00 credit remaining on the card after 25 minutes of calling. How much credit will there be after 33 minutes of calls? <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 #129236 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=129236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of minutes and y=amount of credit remaining\r<BR>\n" );
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document.write( "In order to answer this question, we need to find the equation that models (ie represents) this problem.\r<BR>\n" );
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document.write( "Because \"There is a $23.00 credit remaining on the card after 25 minutes of calling\", this tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=25 ALIGN=MIDDLE  ALT=\"x=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=23 ALIGN=MIDDLE  ALT=\"y=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > which gives the point (25,23). So the line goes through this point.\r<BR>\n" );
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document.write( "Also, since the \"function gives a line with a slope of -0.12\", this tells us that our line has a slope of -0.12. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-0.12 ALIGN=MIDDLE  ALT=\"m=-0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: \"a slope of -0.12\" tells us that for every minute that we talk, we lose $0.12 (or 12 cents).\r<BR>\n" );
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document.write( "If you want to find the equation of line with a given a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.12 ALIGN=MIDDLE  ALT=\"-0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" > which goes through the point (25,23), simply use the point-slope formula to find the equation:\r<BR>\n" );
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document.write( "---Point-Slope Formula---\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_{1},y_{1}\right)\"> is the given point\r<BR>\n" );
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document.write( "So lets use the Point-Slope Formula to find the equation of the line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-23=-0.12%28x-25%29 ALIGN=MIDDLE  ALT=\"y-23=-0.12%28x-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-0.12 ALIGN=MIDDLE  ALT=\"m=-0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=25 ALIGN=MIDDLE  ALT=\"x%5B1%5D=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=23 ALIGN=MIDDLE  ALT=\"y%5B1%5D=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values are given)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-23=-0.12x%2B%28-0.12%29%28-25%29 ALIGN=MIDDLE  ALT=\"y-23=-0.12x%2B%28-0.12%29%28-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.12 ALIGN=MIDDLE  ALT=\"-0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-23=-0.12x%2B3 ALIGN=MIDDLE  ALT=\"y-23=-0.12x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.12 ALIGN=MIDDLE  ALT=\"-0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.12x%2B3%2B23 ALIGN=MIDDLE  ALT=\"y=-0.12x%2B3%2B23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 23 to both sides to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.12x%2B26 ALIGN=MIDDLE  ALT=\"y=-0.12x%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms<BR>\n" );
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document.write( "So the equation of the line with a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.12 ALIGN=MIDDLE  ALT=\"-0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" > which goes through the point (25,23) is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.12x%2B26 ALIGN=MIDDLE  ALT=\"y=-0.12x%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that the equation tying together the amount remaining \"y\" and the number of minutes \"x\" is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.12x%2B26 ALIGN=MIDDLE  ALT=\"y=-0.12x%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<h4>How much credit will there be after 33 minutes of calls?</h4>\r<BR>\n" );
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document.write( "To answer this question, we'll use the equation we just found.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.12x%2B26 ALIGN=MIDDLE  ALT=\"y=-0.12x%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.12%2833%29%2B26 ALIGN=MIDDLE  ALT=\"y=-0.12%2833%29%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=33 ALIGN=MIDDLE  ALT=\"x=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3.96%2B26 ALIGN=MIDDLE  ALT=\"y=-3.96%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=22.04 ALIGN=MIDDLE  ALT=\"y=22.04\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So after 33 minutes of calls, there will be $22.04 of credit left.  </SPAN>\n" );
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