Suppose two variables are directly related. If one variable rises, then the other variable:
a. also rises.
b. falls.
c. remains unchanged.
d. reacts unpredictably.
The correct answer and explanation is :
Correct Answer: a. also rises.
Explanation:
When two variables are directly related, an increase in one results in an increase in the other, and a decrease in one results in a decrease in the other. This type of relationship is known as a direct or positive correlation.
Mathematically, if ( x ) and ( y ) are directly related, they can be represented as:
[
y = kx
]
where ( k ) is a positive constant. This equation indicates that as ( x ) increases, ( y ) also increases proportionally. Similarly, if ( x ) decreases, ( y ) also decreases.
Real-World Examples:
- Speed and Distance – If a car increases its speed while maintaining the same travel duration, the distance covered increases.
- Study Time and Grades – Generally, the more time a student spends studying, the higher their grades.
- Work Hours and Salary – If an hourly wage worker works more hours, their total earnings increase.
Graphical Representation:
The graph of a direct relationship is a straight line that slopes upward from left to right, showing a positive correlation.
