document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=714737>Question 714737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Highway bridges often have expansion joints- small gaps between the bridge sections-that allow for the expansion of the bridge when the weather gets hot. Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75°F and that gap increases to 1 inch when the temperature is 50°F . Assume that there is a linear relationship between the width of the gap and the temperature.<BR>\n" );
document.write( "1. Write an equation that expresses the width of the gap (W) as a function of the temperature (T).<BR>\n" );
document.write( "I need HELP!!! Please I BEG OF U PLEASE HELP!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438953 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=438953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = gap width in inches and y = temperature in Fahrenheit\r<BR>\n" );
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document.write( "\"Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75°F\" means x = 1/2 and y = 75\r<BR>\n" );
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document.write( "\"and that gap increases to 1 inch when the temperature is 50°F \" means x = 1 and y = 50\r<BR>\n" );
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document.write( "Let's find the slope of the line through these two points\r<BR>\n" );
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document.write( "Slope: \r<BR>\n" );
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document.write( "m = (y2 - y1)/(x2 - x1)\r<BR>\n" );
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document.write( "m = (50 - 75)/(1 - 1/2)\r<BR>\n" );
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document.write( "m = (-25)/(1/2)\r<BR>\n" );
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document.write( "m = -50\r<BR>\n" );
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document.write( "So the slope is m = -50\r<BR>\n" );
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document.write( "Now use this to find the equation \r<BR>\n" );
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document.write( "y = mx + b\r<BR>\n" );
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document.write( "y = -50x + b ... plug in the slope we just found\r<BR>\n" );
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document.write( "50 = -50(1) + b ... plug in x = 1 and y = 50\r<BR>\n" );
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document.write( "50 = -50 + b\r<BR>\n" );
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document.write( "50 + 50 = b\r<BR>\n" );
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document.write( "100 = b\r<BR>\n" );
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document.write( "b = 100 \r<BR>\n" );
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document.write( "So the equation is y = -50x + 100 \r<BR>\n" );
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document.write( "Replace x with W since x = gap and y with T because y = temp to get\r<BR>\n" );
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document.write( "T = -50W + 100\r<BR>\n" );
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document.write( "Now solve for W (because we want an equation that expresses the width of the gap (W) as a function of the temperature (T))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+-50W+%2B+100 ALIGN=MIDDLE  ALT=\"T+=+-50W+%2B+100\"   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=T-100+=+-50W ALIGN=MIDDLE  ALT=\"T-100+=+-50W\"   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=-50W+=+T-100 ALIGN=MIDDLE  ALT=\"-50W+=+T-100\"   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=W+=+%28T-100%29%2F%28-50%29 ALIGN=MIDDLE  ALT=\"W+=+%28T-100%29%2F%28-50%29\"   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=W+=+-%28T%2F50%29%2B100%2F%2850%29 ALIGN=MIDDLE  ALT=\"W+=+-%28T%2F50%29%2B100%2F%2850%29\"   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=W+=+-T%2F50%2B2 ALIGN=MIDDLE  ALT=\"W+=+-T%2F50%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+-T%2F50%2B2 ALIGN=MIDDLE  ALT=\"W+=+-T%2F50%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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