Final answer:
Releasing the 'other things equal' assumption in studying the relationship between two variables on a graph results in data points becoming more randomly scattered, due to the influence of additional factors.
Step-by-step explanation:
When considering the relationship between two variables without the 'other things equal' assumption, you would expect the data points representing that relationship to become more randomly scattered (Option D). This is because 'other things equal' implies that all other variables except for the two being considered are held constant. When this assumption is released, other factors may influence the relationship, causing variation that did not exist under the controlled condition, leading to a less clear and more scattered pattern on the graph representing that relationship.
Releasing the 'other things equal' condition would not necessarily change the line's position on the graph directly, nor would it inherently change the relationship from inverse to direct or direct to inverse. Such specific changes in the type of relationship (A, B, C) would require additional information indicating how the additional factors interact with the existing variables to justify changing the nature of the relationship itself. The concept of a linear relationship between two variables is well-described by the linear equation y = mx + b, where m represents the slope of the line and b is the y-intercept.