Quick
Proportionality is typically between two variables, where if one increases the other also increases. Conversely, if one variable decreases, so does the other. These two variables are related by a constant k which is called the constant of proportionality.
proportionality constant is used to relate two variables together, in order to develop a relationship between them, without it, the two variables are merely proportional to each other.
Equations
| Proportional | |
| Inversely Proportional | |
where k is the constant of proportionality
Details
for example, if oranges are 40 cents per pound, then the price, p, is proportional to the weight, w, as given by the function: p = f(w) = 40w which says that the price is equal to a function of the weight which is equal to 40 times the weight. Also, the area, A, of a circle is proportional to the square of the radius, r as given in the equation: A = f(r) = πr2
y is directly proportional to x if there is a constant k such that:
y = kx
where k is called the constant of proportionality
A quantity is inversely proportional to another if one is proportional to the reciprocal of the other. For example, the speed, u, at which a 40-mile trip is made is inversely proportional to the time, t, taken, because u is proportional to 1 over t or 1/t:
This makes sense, the faster the speed, the shorter the time to reach the destination.
Notice that if y is directly proportional to x, then the magnitude of one variable increases when the magnitude of the other increases, and similarly, the magnitude of one variable decreases when the magnitude of the other decreases. If, however, y is inversely proportional to x, then the magnitude of one variable increases when the value of the other decreases.