Final answer:
A proportional relationship is when two variables increase or decrease at the same rate, either directly or inversely. A directly proportional relationship results in a straight line through the origin on a graph, while an inversely proportional relationship results in a curve on the graph.
Step-by-step explanation:
A proportional relationship is a mathematical concept where two quantities increase or decrease at the same rate. In a directly proportional relationship, as one variable increases, the other variable increases at a constant rate. This can be represented by y = kx, where k is the proportionality constant, and if plotted on a graph, this relationship will display as a straight line through the origin (0, 0).
On the other hand, an inversely proportional relationship occurs when one variable increase while the other decreases. This is captured by the equation y = k/x, where k is again a constant. The graph of two inversely proportional variables will be a curve that never cuts the axis.
An example of a directly proportional relationship is when your income is tied to the number of hours you work, such as earning $2.50 for each call you make. This is summarized by p = A x n, where p is pay and n is the number of calls. Constants of proportionality, like the A in the pay-per-call example, help us understand the specific rate at which quantities are related.