Final answer:
A proportional relationship in math signifies that two quantities vary at the same rate, which can be directly proportional (both quantities increase or decrease together) or inversely proportional (one quantity increases as the other decreases). The proportional constant (k) links the changes in these quantities.
Step-by-step explanation:
In mathematics, a proportional relationship is one where two quantities increase or decrease at the same rate. If we have two variables x and y, they are said to be directly proportional if a change in one leads to a proportional change in the other, represented by the equation y = kx, where k is the proportionality constant. Conversely, x and y are inversely proportional if an increase in one results in a proportional decrease in the other, which can be expressed with the equation y = k/x. A graphical representation of a directly proportional relationship will yield a straight line through the origin, whereas a graph of an inverse proportional relationship will produce a hyperbolic curve.
Constants of proportionality are common within various mathematical relationships. For instance, if your earnings (p) are based on the number of calls (n) you make, with a fixed rate, this can be expressed as p = A x n. Here A represents the constant of proportionality relating the number of calls made to the earnings.