Is linear relationship a direct variation? why or why not?
Assuming that the line is neither vertical or horizontal, it is a direct relationship. It indicates that one variable increases or decreases directly with changes in the other variable. A vertical or horizontal line indicates that one variable does not change at all as the other variable changes.
I hope this helps. Thanks for asking.
To determine whether a linear relationship is a direct variation or not, we need to check if it passes through the origin (0,0).
A direct variation is a type of linear relationship where the dependent variable (y) is directly proportional to the independent variable (x). In other words, as x increases or decreases, y also increases or decreases by a constant ratio.
If the line passes through the origin (0,0), it means that when x is zero, y is also zero, and when x increases or decreases, y increases or decreases proportionally. In this case, the linear relationship is a direct variation.
However, if the line does not pass through the origin, it means that when x is zero, y is not necessarily zero. The relationship between x and y is still linear, but it does not exhibit direct variation because it does not pass through the origin.
So, if the linear relationship passes through the origin (0,0), it is a direct variation. Otherwise, it is a simple linear relationship without direct variation.
I hope this explanation clarifies the concept for you. Feel free to ask if you have any further questions.