Final answer:
The constant of proportionality is the constant 'k' that relates two variables in a proportional relationship, either directly as y = kx or inversely as y = k/x. In practical terms, it determines the rate of increase or decrease between variables, such as pay per number of calls made in a part-time job.
Step-by-step explanation:
The constant of proportionality is the constant 'k' that transforms a proportional relationship into an equation. When we say that two quantities are directly proportional, it implies that as one quantity increases, the other quantity increases at a constant rate and vice versa.
This can be represented by the equation y = kx, where 'y' and 'x' are the quantities in question, and 'k' is the proportionality constant. If we know the value of 'y' for a given 'x', we can solve for 'k'. Similarly, in an inverse proportionality, as one quantity increases, the other decreases, which can be described by the equation y = k/x. The value of 'k' in these equations reflects how much one variable will change in response to a change in the other variable.
In practical terms, if you are working part-time calling alumni for donations and get paid per call, there is a direct proportionality between the number of calls you make, 'n', and the pay you receive, 'p', with the relationship described as p = A x n, where 'A' is the amount paid per call. This is a real-life example of a constant of proportionality where 'A' would be equivalent to 'k' in our general formulation.