**Help with Calculus, obtaining a formula from looking at a graph.?**

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*Okay, so I have to find an equation for the line on the graph. The graph can be found in this link and the needed information is given. They want the answer in y=mx+b form. *

http://www.webassign.net/hgmcalc/1-4-36fig_alt.gif

So I am trying to figure out the answer for the graph in a book. The values are a bit different in the link provided. The only difference is that the book value is log2 rather than log9.

So the answer for log 2 is …

y=3.3219x+1

What I did is take the 1/log2 and that gave me the slope, but for some reason, when I do that with the 1/log9 to get the slope from the online problem, it says it is wrong. Thanks for the help. I really need to understand how they came up with this answer!

you have two points on the line so all you have to do is determine the slope from

m = (y2 – y1)/(x2 – x1)

and then use one of the points in

y = m*x + b

to solve for b and you will have your equation.

Point 1: x = 0 and 10^x = 1 so the point is (0 , 1)

Point 2: x = log(A) and 10^[log(A)] = A so the point is [log(A) , A]

m = [A - 1]/[log(A) - 0] = [A - 1]/log(A)

y = x*[A - 1]/log(A) + b

And use the point (0 , 1)

1 = 0 + b and we have b = 1

So the equation is:

y = x*[A - 1]/log(A) + 1

For A = 2 this gives y = x*[2 - 1]/log(2) + 1 and y = 3.3219x + 1

For A = 9 this gives y = x*[9 - 1]/log(9) + 1 and y = 8.3826x + 1

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