Final answer:
Inverse variation occurs when an increase in one variable leads to a decrease in the other, and vice versa. Direct variation occurs when an increase in one variable leads to an increase in the other, and vice versa.
Step-by-step explanation:
In mathematics, inverse variation and direct variation are types of relationships between variables. Inverse variation occurs when two variables have a relationship where an increase in one variable leads to a decrease in the other, and vice versa. This can be represented by an equation of the form y = k/x, where k is a constant. Direct variation, on the other hand, occurs when two variables have a relationship where an increase in one variable leads to an increase in the other, and vice versa, and can be represented by an equation of the form y = kx, where k is a constant.
For example, let's consider the relationship between the time taken to drive a certain distance and the speed of the car. Inverse variation would occur if the speed increases, the time taken to drive the distance would decrease. Direct variation would occur if the speed increases, the time taken to drive the distance would also increase.