Proportional relationships

Two types of relationships between variables are proportional relationships and inversely proportional relationships.

Proportional relationship. In proportional relationships, when one variable is zero, the other is also zero. They increase together at a constant rate, resulting in a linear (line) relationship.  Proportional relationships can be written as:

y ∝ x

This is the same as saying:

y = (some number)*x

Examples of directly proportional relationships between variables:  

In general form, the mathematical relationship for a proportional relationship between an independent variable (x) and dependent variable (y) is:

y = m*x

m is the slope (or steepness) of the line: the slope is constant

Examples of proportional relationships:  

Acceleration = (constant) * Force (net) 

Distance = (constant speed) * time

Inversely proportional relationship. In inversely proportional relationships, the smallest values of one variable occur with the largest values of the other variable and vice versa. Inversely relationships can be written as:

y ∝ 1/x

This can be written as:

y = (some number, k)/x

Or,

y = k/x

Examples of inversely proportional relationships for different numbers (k's) are shown below. 

Examples of inversely proportional relationships:

y = k/x

Acceleration = (constant force) / mass

Time = (constant distance) / speed