Exercise 1 Page 730

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.

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 $x\text{-}$axis will represent the time that John was driving, and the $y\text{-}$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 $x\text{-}$axis.

In each of the graphs we can see a pattern.

1. In the first case, the longer John drives, the less fuel he has left. This is a negative association.
2. 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.