Final answer:
The equation that shows a proportional relationship is B) y = 3x, because it can be expressed in the form y = kx, which indicates a directly proportional relationship between y and x.
Step-by-step explanation:
The student asks which of the following equations shows a proportional relationship:
- A) y = x/3 + 1
- B) y = 3x
- C) y = 3/x
- D) y = 3x - 1
To determine which equation represents a proportional relationship, we need to look for an equation of the form y = kx, where k is the proportionality constant. Only option B fits this criterion, since it can be re-written as y = (3)x, which shows a directly proportional relationship between y and x with k being 3. A proportional relationship means that as x increases or decreases, y will do the same in a constant ratio, and the graph of the equation will be a straight line passing through the origin (0; 0).