Final answer:
Option B, y = mx, represents direct proportionality since it aligns with the general form y = kx, where 'k' is the constant of proportionality.
Step-by-step explanation:
The question posed is regarding the concept of direct proportionality, which exists when two values increase or decrease together at the same rate, described by the equation y = kx. Here, 'k' is the constant of proportionality.
Reviewing the options:
- A) y = mx² + b for nonzero b: This equation represents a quadratic relationship, not direct proportion.
- B) y = mx: This is the correct equation that represents direct proportionality as it takes the form y = kx, where 'm' serves as the constant of proportionality 'k'.
- C) by = mxy: The presence of the variable 'y' on both sides makes it a non-linear equation.
- D) mxy = mx²: Here, 'y' is not alone on one side, and the relationship is not linear due to different powers of 'x'
- Conclusion:
Therefore, option B, which is y = mx, represents direct proportionality, aligning clearly with the definition of two values changing in the same ratio. The other options either include additional terms or do not properly isolate 'y' as a function of 'x' in a linear relationship.