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Math Help - Express the following equations in a form suitable for drawing a straight line graph

  1. #1
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    Express the following equations in a form suitable for drawing a straight line graph

    Express the following equations in a form suitable for drawing a straight line graph, stating its axes, gradient and vertical intercept.

    1. y = e^(ax + by)
    2. y = (a / b)^(xy + 1)
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  2. #2
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    Re: Express the following equations in a form suitable for drawing a straight line gr

    Assuming that a and b are unknown constants to be determined ?

    For the first relationship, take logs

    \ln(y)=ax+by, and then divide by y, (you could also divide by x, that would lead to an alternative equation),

    \frac{\ln(y)}{y}=a\left(\frac{x}{y}\right)+b.

    Then construct the new variables Y=\ln(y)/y and X=x/y.

    That will give you the straight line Y=aX+b which has a slope of a and an intercept of b.

    You can do a similar thing with the second example.
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  3. #3
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    Re: Express the following equations in a form suitable for drawing a straight line gr

    For the second question, this is what I did:
    lg y = (xy + 1)(lg a - lg b)
    lg y = xy lg a - xy lg b + lg a - lg b
    lg y = (lg a/b)xy + lg a/b

    So the Y-axis = lg y, X-axis = xy, gradient = lg a/b and vertical intercept = lg a/b
    Is this correct?
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  4. #4
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    Re: Express the following equations in a form suitable for drawing a straight line gr

    Yes, that should work.
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