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 :
The correct answer is:
a. also rises.
Explanation:
When two variables are directly related (or positively correlated), it means that an increase in one variable leads to an increase in the other, and a decrease in one leads to a decrease in the other. This relationship can be mathematically expressed as:
[
y = kx
]
where:
- ( y ) and ( x ) are the two related variables,
- ( k ) is a positive constant (also known as the constant of proportionality).
For example, consider the relationship between the amount of hours studied and test scores. If studying more hours leads to higher scores, then the two variables (hours studied and test scores) are directly related.
Real-Life Examples of Direct Relationships:
- Work and Pay: If a worker is paid hourly, then the more hours they work, the higher their total pay.
- Speed and Distance: The faster a car travels (at a constant speed), the greater the distance it covers in a given time.
- Quantity and Cost: If you buy more units of a product at a fixed price per unit, the total cost increases.
Mathematical Representation:
If we graph a direct relationship, we typically get a straight line that slopes upward from left to right. This indicates that as one variable rises, the other also rises.
Common Misconceptions:
Some people may confuse a direct relationship with an inverse relationship, where an increase in one variable causes the other to decrease. However, in an inverse relationship, the equation would take the form:
[
y = \frac{k}{x}
]
where increasing ( x ) decreases ( y ).
In conclusion, when two variables are directly related, an increase in one results in an increase in the other, making option (a) also rises the correct answer.
