please help with inverse variation

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embizze | High School Teacher | (Level 2) Educator Emeritus

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It might help to contrast inverse variation with direct variation.

(1) If two variables are directly related, if one variable increases then the other increases proportionally. For example, the more hours you work, the more you get paid.

If two variables are inversely related, then as one variable increases, the other decreases proportionally. For example, as you get farther away from a sound source, the intensity of the sound decreases.

(2) Algebraically, if two variables are directly related then you could write y=kx, where y and x are directly related, and k is the constant of proportionality. In the example above, k is your pay rate.

If two variables are inversely related, you could write y=k/x or xy=k. For example, as the external pressure decreases, the volume of a balloon increases. Here the k might be a physical attribute of the balloon material.

(3) In a table of values if the variables are directly related the ratio of y:x is constant. The graph will be a straight line through the origin.

In a table of values for inversely related variables, the product of x and y is constant. The graph will be a curve.