The precise definition of this relationship is called the algebraic expression. Suppose we set out to investigate this relationship between density, mass and volume and in order to precisely define this relationship, we do an investigation in a laboratory setting on the relationship between the density of several substances manfested as different objects and the corresponding mass of these objects. If the mass of one object in the set is larger than another object then we would observe that the density of the first object will be correspondingly greater than the second. Notice that I am using the term linear here. Not all direct relationships are linear, but these will be.
Linearity has to do with the one on one increase or decrease of one variable related to another.
For example, the density and mass relationship is a direct relationship in that if one observes one variable between one of the objects in the set of objects being larger in size or value then another object in that set, then one would observe the size or value of the other variable in the first object to be correspondingly larger than the second object assuming all other related variables remain constant during the comparison. However, if I said that if one object has double the value of mass as another object then this leads to an observation that the density of the first object is double the density of the second object ,or if one observes that the mass of one object is half the mass of another object in the set then this leads to the density of the first object being half the density of the second object. If we compare one object that has three times the mass of another object in the set then one finds that the density of the first object is triple the density of the second. THAT is a linear relationship. A linear relationship can be depicted as an equality between two ratios so the so called ratio and proportion method used so commonly in the secondary schools only applies to linear relationships.