document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176248>Question 176248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to figure the rate of change for water temp over a three day period. It is not a constant rate in either direction. Day one is 27(C), day two is 26.5(c), and day three is 26(c). What formula do I use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131370 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=131370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, from the data you provided, you would have to conclude that the change in the temperature over the give time span (3 days) is a linear function.<BR>\n" );
document.write( "How would you come to that conclusion? By simply plotting the given data as points on a graph. Choose the temperature (T) as the dependent variable and the day number as the independent variable, you know, like y is commonly the dependent variable and x is commonly the independent variable.<BR>\n" );
document.write( "So you are given three points which you can express as: (d, T) for ( day No., Temp).<BR>\n" );
document.write( "The three points are:<BR>\n" );
document.write( "(1, 27), (2, 26.5), (3, 26)<BR>\n" );
document.write( "So let's find the slope of the line represented by these points using the standard slope formula (m) and two of the given points:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > but, of course, we will use d (day) instead of x and T (temp) instead of y, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28T%5B2%5D-T%5B1%5D%29%2F%28d%5B2%5D-d%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28T%5B2%5D-T%5B1%5D%29%2F%28d%5B2%5D-d%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Let's use the two points (1, 27) and (3, 26), so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2826-27%29%2F%283-1%29 ALIGN=MIDDLE  ALT=\"m+=+%2826-27%29%2F%283-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying this, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-%281%2F2%29 ALIGN=MIDDLE  ALT=\"m+=+-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we have a negative slope which means the temperature (T) is decreasing with the passage of days, where T = Temp. and d = day number.<BR>\n" );
document.write( "Now we can start the formula using the \"Point-slope\" form of a linear equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx%2Bb ALIGN=MIDDLE  ALT=\"y+=+mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > or, in this problem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+md%2Bb ALIGN=MIDDLE  ALT=\"T+=+md%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+%28-1%2F2%29d%2Bb ALIGN=MIDDLE  ALT=\"T+=+%28-1%2F2%29d%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > But we need to find the value of b, the T-intercept. We can do this by substituting the T- and d-values from any one of the three given points. Let's choose (2, 26.5), so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26.5+=+%28-1%2F2%29%282%29%2Bb ALIGN=MIDDLE  ALT=\"26.5+=+%28-1%2F2%29%282%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify this and solve for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26.5+=+-1%2Bb ALIGN=MIDDLE  ALT=\"26.5+=+-1%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27.5+=+b ALIGN=MIDDLE  ALT=\"27.5+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we can write the final equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28T+=+%28-1%2F2%29d%2B27.5%29 ALIGN=MIDDLE  ALT=\"highlight%28T+=+%28-1%2F2%29d%2B27.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's see what this would look like on a graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-3%2C60%2C-2%2C30%2C%28-1%2F2%29x%2B27.5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-3%2C60%2C-2%2C30%2C%28-1%2F2%29x%2B27.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );