We are asked to describe how we use patterns to compare two quantities. First, note that we can think of different quantities as variables. Now, see that patterns ( or trends) in data can tell us about the relationship between the variables. Consider this example.

John is traveling solo across Arizona. Before he sets off, he makes sure that his tank is full up. The capacity of his tank is $40$ liters. Because John does not plan on making any stops, the entire drive should take him six hours.

See that there are at least three quantities or variables to consider in this example.

The time that John was driving.
The amount of fuel left in the tank.
The distance John drove.

A line graph can be helpful to show how the amount of fuel left changes as John drives across the state. The $x -$ axis will represent the time that John was driving, and the $y -$ axis will be the fuel he had left.

Now, we can also show how the distance that John drove changed during the drive. We will not change the $x -$ axis.

In each of the graphs we can see a pattern.

In the first case, the longer John drives, the less fuel he has left. This is a negative association.
In the second case, the longer John drives, the greater distance he travels. This is an example of negative association.

See that if we notice a pattern in a data set, then we can tell what type of association there is between the variables, or quantities.

Exercise