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