A direct relationship exists when:
a. there is no association between two variables.
b. one variable increases and there is no change in the other variable.
c. one variable increases and the other variable increases.
d. one variable increases and the other variable decreases.
The correct answer and explanation is :
Correct Answer:
c. One variable increases and the other variable increases.
Explanation:
A direct relationship (also known as a positive correlation) occurs when an increase in one variable leads to an increase in another variable. Conversely, when one variable decreases, the other also decreases. This relationship is often represented as a straight or upward-sloping curve on a graph.
For example, consider the relationship between studying time and exam scores. If a student spends more time studying, their exam scores are likely to increase. This suggests a direct relationship because both variables move in the same direction. Similarly, the relationship between the number of hours worked and total income earned is also direct: as the number of work hours increases, total income also rises.
In mathematical terms, a direct relationship is expressed as:
[
y = kx
]
where:
- ( y ) is the dependent variable,
- ( x ) is the independent variable, and
- ( k ) is a positive constant.
This equation shows that as ( x ) increases, ( y ) also increases proportionally.
On the other hand, an inverse (or negative) relationship occurs when one variable increases while the other decreases (option d). For example, as the speed of a car increases, the time taken to reach a destination decreases.
The other options are incorrect because:
- Option (a) describes no relationship at all.
- Option (b) suggests that one variable changes while the other remains constant, which does not describe a relationship.
In summary, a direct relationship means that both variables move in the same direction, making option (c) the correct answer.
