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by Anonymous on July 5th, 2005

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When you have a linear graph with a positive slope the x and y variables are said to be directly proportional, what If you have a linear graph with a negative slope? Is it inversely proportional?

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Answers. 4 helpful answers below.

  • by jalex137 on August 31st, 2005

    jalex137

    I thought the moderators had removed my embarrasingly incorrect answer, but it just turns out that the question is repeated. This has spurred me to look for a correct answer. In my technical field, we sometimes use the term "inversely proportional" in the situation you describe, but that is sloppy at best, and just wrong at worst. I can't find any term for the negative linear slope other than directly proportional. That term seems not to care whether the proportion is positive or negative. I would suggest the term "negatively proportional", but I can't find any mathematical source which uses it. Directly proportional is defined as y being some non-0 multiple of x, and it doesn't seem to matter if that number is positive or negative. So, for example, y = 2x and y = -2x both satisfy the definition. The equation for direct proportionality then, looks like this: y = kx, where the constant k is a rational number (whole number or fraction, positive or negative) other than 0.

    Inverse proportionality, which is also called reciprocal proportionality, is expressed by y = k(1/x), which is not linear.

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  • by Shabba on December 13th, 2005

    Shabba

    Directly proportional means that as value 1 (x) increases, so does value 2 (y), at a set ratio.

    Direct proportion is not dependent upon positive or negative. In maths, a decrease is also known as a "negative increase". This means that the value is increasing in the negative direction. So to get from -1 to -10 you have to negatively increase your number by 9.

    So if y negatively increases at a set rate compared to x negatively increasing, then they would be directly proportional.

    Inversely proportional is the opposite. y decreases as x increases, in either the positive or negative direction.

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  • by Farino on July 15th, 2005

    Farino

    Yes. As one increases the other decreases, thus inversely proportional.

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  • by Kay_T on August 29th, 2010

    Kay_T

    I think so. It makes sense. Just think of inverse as the opposite. Inverse means opposite.

    For relationships with positive slope, Thing1 increases and causes Thing2 to increase. That means that when Thing1 decreases, Thing2 decreases as well.

    Remember: Inverse means the Opposite

    What would be the Opposite to the positive relationship described above?
    Thing2 decreases as Thing1 increases and vice versa.

    This is a negative relationship, being the opposite of the positive.
    Inverse=Opposite=Negative

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