In science and mathematics, an inverse relationship is a
relationship between two variables in which the increase of one value causes
the decrease of the other. Discover the definition of an inverse relationship
and how to graph one.

#### What Is an Inverse Relationship?

Inverse relationships, also known as negative relationships,
exist when two variables have a negative correlation. When one variable rises,
another falls, and vice versa. These are inverse correlations; when one
variable in the data set rises, the other falls. As a result, their ratios
produce a negative number.

Inverse relationships shed light on cause and effect and aid
businesses in forecasting trends. Understanding how one variable affects
another can be useful in developing more efficient and cost-effective
strategies.

#### How to Calculate an Inverse Relationship

When one variable increases, the other variable decreases in
an inverse relationship. An inverse relationship is calculated using the
formula: y = k ÷ x.

Mathematically, x and y represent the two variables, and k
is a constant. As x increases, y decreases, and vice versa. For example, in a
half marathon race, y represents time, k represents the distance, and x
represents the runner’s speed. If speed increases, the time to complete the
race decreases.

#### What Is the Opposite of Inverse Relationship?

An inverse relationship is the inverse of a direct or
proportional relationship. In a direct relationship, an increase in one
variable causes an increase in another variable. On a graph, that would mean
the x-values and y-values move up or down together. For example, the cost of
manufacturing a car and its overall cost to the consumer may reflect a causal
relationship: a higher manufacturing cost leads to a higher price tag for the
buyer.

Variables move in opposite directions in inverse
relationships, or as one moves up, the other moves down, and vice versa.
Consider the relationship between plane travel time and customer comfort: as
one variable (flight time) increases, the other variable (customer comfort)
decreases.

#### 3 Inverse Relationship Examples

Check below for examples of inverse relationships you might
encounter in real life:

**1. Hot weather and soup sales:** People prefer soup in
the cooler months, so soup companies will see a drop in sales as the
temperature rises.

**2. Interest rates and home purchases:** Here, the first
variable is interest rates (x); the second is the rate of home purchases (y).
Low interest rates entice homebuyers, so when x increases, y
decreases.

**3. Unemployment rates and consumer spending:** Higher
unemployment means lower consumer spending. People with less money or less
financial stability are more likely to save, spend less, and make purchases
using coupons and discounts. In the opposite scenario, this would be a positive
correlation: as employment rates rise, consumer spending may rise as well.

#### Inverse Relationship Graph

On a graph, an inverse relationship always has a negative
slope. In general, at least three data points are required to reveal a negative
relationship on a graph. Create a graph on which your x-axis represents one
variable, and the y-axis represents the other. In this example, the x variable
is soup sale revenue in thousands of dollars on a given day, and the y variable
is the daily mean temperature on those days. Your variables might look like
this:

On a fifty-degree day, soup sales were at $1,000, but on a
thirty-degree day, sales were at $3,000. On your chart, you will note a
downward slope, indicating an inverse relationship: when temperatures go down,
soup sales go up.

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