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inverse or
negative relationship is a mathematical relationship in which one
variableIn mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
, say
y, decreases as another, say
x, increases. For a linear (straightline) relation, this can be expressed as
y = abx, where
b is a constant value less than zero and
a is a constant. For example, there is an inverse relationship between education and unemployment — that is, as education increases, the rate of unemployment decreases.
Inverse relationships and their counterpart,
direct relationshipIn mathematics and statistics, a positive or direct relationship is a relationship between two variables in which change in one variable is associated with a change in the other variable in the same direction. For example all linear relationships with a positive slope are direct relationships...
s, are widely used in the
physical sciencePhysical science is an encompassing term for the branches of natural science and science that study nonliving systems, in contrast to the life sciences...
s to describe the relationship between two variables in an equation.
In
economic graphThe social science of economics makes extensive use graphs to better illustrate the economic principles and trends it is attempting to explain. Those graphs have specific qualities that are not often found in other sciences.A common and specific example is the Supply and Demand graph shown at right...
ing, two variables are said to have an inverse relationship if the graph line slopes downward to the right.