document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140997>Question 140997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The director of a summer day cmp estimates that 100 children will join if the camp fee is 250.00, but for each 20.00 decrease in the fee, ten more children will enroll.<BR>\n" );
document.write( "Determine the linear equation tha will represent the number of children who will enroll a a given fee.\r<BR>\n" );
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document.write( "Graph the linear equatin that rpresens the number of children who will enroll at a given fee.\r<BR>\n" );
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document.write( "How many students will enroll if the camp fee is 180.00?\r<BR>\n" );
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document.write( "How many studens will enroll if the camp is free? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102665 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102665\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The director of a summer day camp estimates that 100 children will join if the camp fee is 250.00, but for each 20.00 decrease in the fee, ten more children will enroll.<BR>\n" );
document.write( "Determine the linear equation that will represent the number of children who will enroll a a given fee.<BR>\n" );
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document.write( "Let x = cost per child<BR>\n" );
document.write( "Let y = no. of children enrolled<BR>\n" );
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document.write( "From the information given, derive two set of  x/y coordinates<BR>\n" );
document.write( "100 kid at $250: x1=250, y1=100<BR>\n" );
document.write( "and<BR>\n" );
document.write( "110 kids at $230: x2=230, y2=110<BR>\n" );
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document.write( "Find the slope using the slope equation: m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28110-100%29%2F%28230-250%29 ALIGN=MIDDLE  ALT=\"%28110-100%29%2F%28230-250%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%28-20%29 ALIGN=MIDDLE  ALT=\"10%2F%28-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use the point/slope equation: y -y1 = m(x-x1)<BR>\n" );
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document.write( "y - 100 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 250)<BR>\n" );
document.write( "y - 100 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 125<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 125 + 100<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 225; is the linear equation <BR>\n" );
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document.write( "Graph the linear equation that represents the number of children who will enroll at a given fee.<BR>\n" );
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document.write( "Graph y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 225,<BR>\n" );
document.write( "To graph this, use an x scale of 0 to +450, and y scale from 0 to 300<BR>\n" );
document.write( "(we are not interested in any neg values here)\r<BR>\n" );
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document.write( "You only need two pair of coordinates to plot a linear (straight line) graph<BR>\n" );
document.write( "However here are three sets: we will find y for x = 100, x = 200, x = 250<BR>\n" );
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document.write( "Substitute 100 for x, in the equation y = -.5x + 225 and find y<BR>\n" );
document.write( "y = -.5(100) + 225<BR>\n" );
document.write( "y = -50 + 225<BR>\n" );
document.write( "y = +175<BR>\n" );
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document.write( "If we were making a table for x/y values, it would be:<BR>\n" );
document.write( " x | y<BR>\n" );
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document.write( "100|175<BR>\n" );
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document.write( "Substitute 200 for x and find y:<BR>\n" );
document.write( "y = -.5(200) + 225<BR>\n" );
document.write( "y = -100 + 225<BR>\n" );
document.write( "y = +125<BR>\n" );
document.write( "now our table is:<BR>\n" );
document.write( " x | y<BR>\n" );
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document.write( "100|175<BR>\n" );
document.write( "200|125<BR>\n" );
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document.write( "Substitute 250 for x, find y<BR>\n" );
document.write( "y = -.5(250) + 225<BR>\n" );
document.write( "y = -125 + 225<BR>\n" );
document.write( "y = +100<BR>\n" );
document.write( "we have:<BR>\n" );
document.write( "x | y<BR>\n" );
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document.write( "100|175<BR>\n" );
document.write( "200|125<BR>\n" );
document.write( "250|100<BR>\n" );
document.write( " 0 |225, note this is the y intercept (the camp is free, 225 kids)<BR>\n" );
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document.write( "Plot these 4 points, join them with straight lines<BR>\n" );
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document.write( "it should look like this: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-50%2C+450%2C+-50%2C+275%2C+-.5x%2B225%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-50%2C+450%2C+-50%2C+275%2C+-.5x%2B225%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "How many students will enroll if the camp fee is 180.00?<BR>\n" );
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document.write( "substitute 180 for x in our equation and find y<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(180) + 225<BR>\n" );
document.write( "6 = -90 + 225 <BR>\n" );
document.write( "y = +135 will enroll<BR>\n" );
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document.write( "How many students will enroll if the camp is free?<BR>\n" );
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document.write( "In this case x = 0<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(0) + 225<BR>\n" );
document.write( "y = 225 enrolled if it is free, you can see on the graph, that's the y intercept<BR>\n" );
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document.write( "did this make sense to you, any questions? </SPAN>\n" );
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