Which of the following statements is correct?
a. Slope is the ratio of the vertical change (the rise or fall) to the horizontal change (the run).
b. A direct relationship is one in which two variables change in the same direction.
c. An inverse relationship is one in which two variables change in opposite directions.
d. An independent relationship is one in which two variables are unrelated.
e. All of these.
The correct answer and explanation is :
The correct answer is:
e. All of these.
Explanation:
Each of the statements provided is correct. Let’s analyze them one by one:
- Slope Definition (Statement a)
The slope of a line in mathematics and physics is defined as the ratio of the vertical change (rise or fall) to the horizontal change (run). Mathematically, it is given by:
[
\text{slope} = \frac{\text{rise}}{\text{run}}
]
This formula helps determine how steep a line is on a graph. - Direct Relationship (Statement b)
A direct relationship means that when one variable increases, the other also increases, and when one decreases, the other decreases. This is often represented by a positive slope in a graph. For example, in physics, Ohm’s Law (( V = IR )) shows that voltage and current have a direct relationship when resistance is constant. - Inverse Relationship (Statement c)
In an inverse relationship, when one variable increases, the other decreases, and vice versa. Mathematically, this is represented as:
[
y \propto \frac{1}{x}
]
A common example is Boyle’s Law in physics, where pressure and volume have an inverse relationship. - Independent Relationship (Statement d)
When two variables are independent, they do not affect each other. For example, the amount of sunlight in a day does not affect the number of pages in a book.
Since all the statements are correct, option (e) All of these is the correct answer.
