What Is the Difference Between a Direct and an Inverse Relationship?

By Ariel Balter
An upward curve is an example of direct relationship, but not direct proportion.
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There are many ways that changing one part of a system will cause another part to change. For example, the rotation of the Earth causes a daily cycle of light and temperature changes, and the stock market changes with time. In general, two variables in a system represented by x and y can be related by a function: y = f(x). There are two special types of relationship, direct and inverse.

Direct Relationships

When y always changes in the same way as x, either up or down, they are in direct relationship. When people consume fewer calories, for instance, their weight goes down and when students study more, their grades go up. These are direct relationships.

Inverse Relationships

When a solution evaporates, the volume of solution goes down, but the concentration goes up. Increasing the amount of insulation in a house reduces the energy needed for heating and cooling. These are inverse relationships.

Proportionality vs. Relationship

In math and science, proportionality is a special case of direct and inverse relationship. Two variables, x and y, are in direct proportion if y is equal to a constant A times x: y = Ax. A can be positive or negative. Two variables, x and y, are in inverse proportion if y is directly proportional to 1/x: y = A/x. An example of an equation with both direct and inverse relationships is Ohm’s law from electricity. Ohm’s law states that the current is equal to the voltage divided by resistance. In this equation, current is directly proportional to voltage, but inversely proportional to resistance.

About the Author

Ariel Balter started out writing, editing and typesetting, changed gears for a stint in the building trades, then returned to school and earned a PhD in physics. Since that time, Balter has been a professional scientist and teacher. He has a vast area of expertise including cooking, organic gardening, green living, green building trades and many areas of science and technology.