Two related quantities x and y are called proportional (or directly proportional) if there exists a constant non-zero number k such that
- y = kx
In this case, k
is called the proportionality constant
of the relation. If y
are proportional, we often write
- y ~ x.
For example, if you travel at a constant speed, then the distance you cover and the time you spend are proportional, the proportionality constant being the speed. Similarly, the amount of force
acting on a certain object from the gravity
of the Earth
at sea level is proportional to the object's mass
To test whether x and y are proportional, one performs several measurements and plots the resulting points in a Cartesian coordinate system. If the points lie on (or close to) a straight line passing through the origin (0,0), then the two variables are proportional, with the proportionality constant given by the line's slope.
The two quantities x and y are inversely proportional if there exists a non-zero constant k such that
- y = k/x
For instance, the number of people you hire to shovel sand is (approximately) inversely proportional to the time needed to get the job done.
See also: proportional font, proportional representation