# What is the word to describe an opposite changing relation between two variables?

For example in y=1/x, variable y and x are inversely proportional.

If y and x have a different relation than inversely proportional, but still y decreases as x increases and vice versa, how do you describe their relation? Thanks!

• Drop the "proportional" and just refer to it as an inverse relationship.' – Jim Mar 6 '14 at 4:15

Inversely proportional doesn't only describe the direct 1/x case, but the general case where y decreases when x increases. So even if you had a formula like:

``````y = 12 + 57/(2x + 5)
``````

or

``````y = 1/x^2
``````

You would still describe the relationship between y and x as inversely proportional.

• A mathematically proportional relationship requires that the change be related by a constant multiplier, not just moving in opposite or the same directions. – ColleenV parted ways Nov 6 '14 at 21:48

"Monotonically decreasing" describes a situation where (as x goes up) y either stays the same or goes down. For "continuous functions", this is the same as saying that dy/dx <= 0.