Posted by ladybug on Friday, November 2, 2012 at 11:02pm.
rate of change is (change in y)/(change in x)
f(5) = 12
f(7) = 20
y changes from 12 to 20 as x changes from 5 to 7:
rate of change is thus (20-12)/(7-5) = 8/2 = 4
Note that the rate of change is the same as the slope of the line f(x)=4x-8
The secant line is thus the line from (5,12) to (7,20). Or, it is the line from (5,12) with a slope of 4. Either way, you get
(y-12) = 4(x-5)
y = 4x -8
This is not surprising, since the secant joining any two points on a line is just a section of the same line.
It strikes me as odd that such a problem is posed. Could it be that the function is
f(x) = 4^x-8. Probably not, as the values of f(x) would be quite large.
Oh well, if the function is wrong, just use the method above to find the secant.
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