Question

Distinguish between inversely and directly proportional relationships.

a) In directly proportional relationships, one variable increases as the other decreases. In inversely proportional relationships, both variables change in the same direction.
b) In inversely proportional relationships, one variable increases as the other decreases. In directly proportional relationships, both variables change in the same direction.
c) In both inversely and directly proportional relationships, one variable increases as the other decreases.
d) In both inversely and directly proportional relationships, both variables change in the same direction.

Answer 1

In inverse proportionality, one variable increases as the other decreases (more-less relationship), whereas in direct proportionality, both variables increase or decrease together (more-more relationship).

Step-by-step explanation:

To distinguish between inversely and directly proportional relationships, we must understand how each type of proportionality affects the variables in question:

• Inversely proportional relationships are characterized by one variable increasing as the other decreases. This relationship is defined by the equation y = k/x, where k is a constant proportionality factor. In such relationships, when one variable is multiplied by a number, the other must be divided by the same number, showing a 'more-less' relationship.
• Directly proportional relationships mean that as one variable increases, the other variable increases by the same factor, or conversely, as one decreases, so does the other. This 'more-more' relationship is represented by the equation y = kx, where k is the constant of proportionality.

Graphically, inverse proportionality produces a curve that never cuts the axis, while direct proportionality results in a straight line through the origin.