Question 176248: 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?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! 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.
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.
So you are given three points which you can express as: (d, T) for ( day No., Temp).
The three points are:
(1, 27), (2, 26.5), (3, 26)
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:
 but, of course, we will use d (day) instead of x and T (temp) instead of y, so...
 Let's use the two points (1, 27) and (3, 26), so...
 Simplifying this, we get:
 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.
Now we can start the formula using the "Point-slope" form of a linear equation:  or, in this problem,  , so we can write:
 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...
 Simplify this and solve for b.
 Add 1 to both sides.
 Now we can write the final equation.
Let's see what this would look like on a graph:
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