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Chapter 13: Problem 12

Two variables \(x\) and \(y\) have a negative linear relationship. Explain what happens to the value of \(y\) when \(x\) increases. Give one example of a negative relationship between two variables.

Short Answer

Expert verified
In a negative linear relationship between \(x\) and \(y\), \(y\) decreases as \(x\) increases. An example is the relationship between time spent studying and number of errors on a test where more study time leads to fewer errors.

Step by step solution

01

Understand Negative Linear Relationship

A negative linear relationship between two variables implies that as one variable increases, the other decreases at a consistent rate. Thus, if \(x\) increases in a negative linear relationship, \(y\) would decrease.
02

Example of Negative Linear Relationship

An example could demonstrate this: for instance, consider the relationship between time spent studying and number of errors on a test. Theoretically, as time studying (variable \(x\)) increases, the number of errors on a test (variable \(y\)) would decrease. This illustrates a negative linear relationship.

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