Question

In a relationship with two variables, when one variable becomes larger by a given factor and the other becomes smaller by the same factor, the variables are said to be________related

a) inversely
b) equally
c) Directly

Answer 1

One variable goes up while the other goes down that's what you call an inverse relationship.

Equally means if one variable goes up by some amount the other must as well. same if they go down.

Take the following for example:

The relationship between pressure and volume.

\[P _{1}V _{1} = P _{2}V_{2}\]

Say if P1 and V1 are some known value.
if I increase say P2 by some amount then V2 must go down, because what that expression says is that the product of the two variables must be a constant.

An example of a direct relationship is that one variable increases and the other one does as well.

\[y = mx\]

an equation of a line, (x) and y are both directly related because if you multiply x by m y will go up by a factor of m.

Answer 2

equal and directly kind of imply the same thing.. at least from my understanding @raysa