Final answer:
In a direct or linear relationship, as one variable increases, the other variable also increases, like in the linear and angular velocity relationship in physics where they are directly proportional.
Step-by-step explanation:
In a direct or linear relationship, as one variable increases, what happens to the other variable? The other variable increases because, in a direct or linear relationship, both variables move in the same direction. This can be represented graphically as a straight line with a positive slope. If one variable is directly proportional to another variable, as one increases, so does the other.
For instance, in physics, if we look at angular and linear velocity, we see this direct relationship play out. The linear velocity of a point on an object is directly proportional to the angular velocity of that object. Therefore, when the angular velocity increases, the linear velocity increases as well. This is because the linear velocity (v) is calculated by the product of the angular velocity (ω) and the radius (r) of the circle through which the point moves (v = ω*r), proving their directly proportional relationship.
Moreover, it's essential to differentiate between variables in these relationships. An independent variable is the one that is changed or manipulated, while a dependent variable is the one that is measured and is thought to change in response to the independent variable. In the case of velocity, if the angular velocity is the independent variable, then the linear velocity is the dependent variable that changes in direct response.