document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998962>Question 998962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The speed of sound in air changes with the temperature. When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second. For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. (Round your answers to two decimal places.)\r<BR>\n" );
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document.write( "(a) Explain why speed S is a linear function of temperature T.<BR>\n" );
document.write( "Because S always increases by 1.1 when T increases by ...., S has a constant rate of change and is a linear function of T.\r<BR>\n" );
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document.write( "Identify the slope of the function.<BR>\n" );
document.write( ".....\r<BR>\n" );
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document.write( "(b) Use a formula to express S as a linear function of T.<BR>\n" );
document.write( "S =  .....\r<BR>\n" );
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document.write( "(c) Solve for T in the equation from part (b) to obtain a formula for temperature T as a linear function of speed S.<BR>\n" );
document.write( "T =  .....\r<BR>\n" );
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document.write( "(d) Explain in practical terms the meaning of the slope of the function you found in part (c).<BR>\n" );
document.write( "The slope of T as a linear function of S is ..... , and this means that an increase in the speed of sound by 1 foot per second corresponds to an increase of ..... degree in temperature.<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 #616648 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=616648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are really interested in making the equation to relate T and S.  Think of the format of the model to be like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=mT%2Bb ALIGN=MIDDLE  ALT=\"S=mT%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > for general points  (T,S).  That equation for S is in slope-intercept form.\r<BR>\n" );
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document.write( "One point described is  (32, 1087.5).<BR>\n" );
document.write( "The slope, m, is described as positive, relating  1.1 feet per second with 1 degree Fahrenheit, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1.1 ALIGN=MIDDLE  ALT=\"m=1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Your choice to form the more specific equation.  You can either use point-slope form, or you can use slope-intercept form.\r<BR>\n" );
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document.write( "Here, the work will stay in slope-intercept form  (but not need to do so).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=mT%2Bb ALIGN=MIDDLE  ALT=\"S=mT%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S-mT=b ALIGN=MIDDLE  ALT=\"S-mT=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=S-mT ALIGN=MIDDLE  ALT=\"b=S-mT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute the known point and slope:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1087.5-1.1%2A32 ALIGN=MIDDLE  ALT=\"b=1087.5-1.1%2A32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1052.3 ALIGN=MIDDLE  ALT=\"b=1052.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Final formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28S=1.1%2AT%2B1052.3%29 ALIGN=MIDDLE  ALT=\"highlight%28S=1.1%2AT%2B1052.3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The formula can easily be solved for T as a function of S. </SPAN>\n" );
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