Final answer:
Only option a (m = 1/5n) represents a proportional relationship because it can be expressed in the form y = kx with k being a constant of proportionality and no extra constants added.
Step-by-step explanation:
The question pertains to identifying which equations represent proportional relationships. An equation represents a proportional relationship if it can be expressed in the form y = kx, where k is the constant of proportionality. Let's examine the options provided:
- a. m = 1/5n: This is a proportional relationship because it can be rewritten as m = (1/5)*n, fitting the form of y = kx with k = 1/5.
- b. 2x = y + 1: This is not a proportional relationship because it has an extra constant being added, which does not fit the proportional form y = kx.
- c. 2/3 + a = b: This is also not a proportional relationship as it does not align with the form y = kx due to the constant 2/3.
- d. 4/8=1/2: This is just a numerical equation showing equality between two fractions and does not establish a proportional relationship between two variables.
Thus, among the given options, only option a represents a proportional relationship.