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In this problem, x cubed = 12y...how do you solve to determine if this is direction variation or not?

  • Math -

    This can be reduced to 12y=x³, or
    y=x³/12

    Direct variation have two properties:
    1. it passes through the origin, i.e. if x=0, y=0.
    This property is satisfied by the above equation.
    2. x and y are both linear, i.e. if you multiply x by any finite number, y increases by the same ratio.
    For example, for the above,
    x=1, y=1/12
    x=2, y=8/12 (y is increased 8 times instead of 2), so the equation is not a direct variation.

    Example of a direct variation:
    y=2x
    x=1, y=2
    x=2, y=4
    x=7, y=14
    So the ratios are always 2:
    2/1 = 4/2 = 14/7 =2 (equals the coefficient of x).

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