Final answer:
The equation y = k/x signifies an inverse proportionality where 'y' decreases as 'x' increases, with 'k' being a constant. It demonstrates how the product of 'y' and 'x' remains unchanged, in contrast to the direct proportionality represented by y = kx.
Step-by-step explanation:
The equation y = k/x, represents an inverse proportionality between two variables, where 'y' is the dependent variable, 'x' is the independent variable, and 'k' is the constant of proportionality. In this relationship, as 'x' increases, 'y' decreases in such a way that their product remains constant, specifically equal to 'k'. This contrasts with a directly proportional relationship, exemplified by the equation y = kx, where 'y' increases directly as 'x' increases and the proportionality constant 'k' determines the rate of increase.
In summary, in an inverse proportionality, 'y' and 'x' change in opposite directions while maintaining a constant product. This is distinct from a linear relationship (e.g., y = mx + b), which is represented by a straight line when graphed, and exponential relationships where the rate of growth increases as the value of the dependent variable gets larger.