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Math Help - Help with direct & inverse variations

  1. #1
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    Help with direct & inverse variations

    I understand the basics of variations, but am having trouble when numbers are applied. For example, I have the following problem:

    "Assume that y is directly proportional to x. Use the given x-value and y-value to find a linear model that relates y and x.
    x = 9, y = 36 "

    How do I find the linear model?

    The same goes for this problem:

    "Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) y is inversely proportional to x. (y = 7 when x = 32.)"

    Any help is greatly appreciated. Thanks
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by 305boy View Post
    I understand the basics of variations, but am having trouble when numbers are applied. For example, I have the following problem:

    "Assume that y is directly proportional to x. Use the given x-value and y-value to find a linear model that relates y and x.
    x = 9, y = 36 "

    How do I find the linear model?

    The same goes for this problem:

    "Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) y is inversely proportional to x. (y = 7 when x = 32.)"

    Any help is greatly appreciated. Thanks

    Directly proportional means y = k x for some constant k. Plugging in those numbers you get:
    36 = k 9

    Find k = 4

    So the model is y= 4x

    Good luck!
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  3. #3
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    skeeter's Avatar
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    Quote Originally Posted by 305boy View Post
    I understand the basics of variations, but am having trouble when numbers are applied. For example, I have the following problem:

    "Assume that y is directly proportional to x. Use the given x-value and y-value to find a linear model that relates y and x.
    x = 9, y = 36 "

    y is directly proportional to x ... y = kx

    y = 4x ... would be a linear equation, right?


    The same goes for this problem:

    "Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) y is inversely proportional to x. (y = 7 when x = 32.)"

    y is inversely proportional to x ... \textcolor{red}{y = \frac{k}{x}}

    \textcolor{red}{y = \frac{224}{x}}
    ...
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