Question

how is it possible that all proportional relationships are linear functions but not all linear functions are proportional relationships

Answer 1

proportional relationship is just a linear relationship where the line passes through the origin (0, 0).

Answer 2

Explanation:

A line that passes through the origin is proportional (y = mx). But a line that doesn't pass through the origin isn't proportional (y = mx + b). So all proportional relationships are linear, but not all linear relationships are proportional.