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# Alice and Bob take some samples of (x,y) and get (1,2), (10,9) and (100,16). They note that comparing log 10(x) to y, the translated points?

... (0,2), (1, 9) and (2,16) all sit on a straight line.

A) find the equation of the straight line in terms of y and log10(x).

B) use your straight line equation to find the original equation

### 1 Answer

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- Keith ALv 61 month ago
First, note that log_10 (x) would be better notation. The space between 10 and x is essential; the parentheses not, here.

(The points do not need to be translated; they lie on a line, anyway)

Put s = log_10 x, for convenience in writing.

Then we have the three pairs

Using the first two points:

gradient = (9 - 2) / (2 - 1) = 7

(in terms of y, not y - 1)

So the equation is

y -2 = 7 (z - 0) .

I.e., y = 2 + 7 log_10 x

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