If two quantities are directly proportional to one another, that is, for example, as one increases, the other increases proportionately. So, if one doubles then the other also doubles.
Mathematically we can write y=kx, where the two quantities are y and x. y varies directly in proportion to x, and the constant of proportionality is k. k=y/x and is constant for all x-y pairs. Graphically this is a straight line passing through the origin and k is the slope. k can be positive or negative but not zero. k can be bigger than 1 or smaller than 1. For example, the circumference of a circle is proportional to its radius. In this case k=2π. Purchase tax could be another example. If purchase tax is 12% the tax T is proportional to the value V of an item, so T=0.12V, (k=0.12) and the cost to the customer would be V+0.12V. Another example is found on a map drawn to scale. If the scale is 1 inch to represent a mile (63,360 inches) and the map measurement is x inches, y=63360x or x miles (k=63360).
Note that temperature conversion Celsius to Fahrenheit is NOT a direct proportionality because 0°C is not 0°F.