Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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

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  • 1 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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