Final answer:
Only Equation 2 (y = 3/4x) shows a proportional relationship as it has the form y = mx, with no additional constant term. The other equations either include an added constant or represent a non-linear relationship, thus not indicating direct proportionality.
Step-by-step explanation:
The student's question asks which equations would produce a proportional relationship. A proportional relationship is characterized by a straight-line graph that passes through the origin. In the form y=mx, where m is the constant of proportionality, the equation represents a direct proportion between y and x when there is no added constant term.
- Equation 1: y = x - 3 is not proportional because it has a y-intercept other than zero.
- Equation 2: y = 3/4x is proportional as it only involves a multiplication factor and no additional constant; y changes directly as x changes.
- Equation 3: y = 2x + 5 is not proportional due to the added constant term (+5), which means the line does not pass through the origin.
- Equation 4: y = 5x² represents a quadratic, not linear, relationship so it is not proportional.
Hence, only Equation 2 shows a proportional relationship.