Final answer:
The equation representing a proportional relationship is A) y = -x, as it is the only option that fits the form y = kx, where k is the constant of proportionality, and passes through the origin.
Step-by-step explanation:
The question asks which equation represents a proportional relationship. A proportional relationship between two variables x and y can be represented by the equation y = kx, where k is the proportionality constant and the graph of the equation is a straight line passing through the origin (0, 0). Looking at the options:
- A) y = -x is a proportional relationship because it fits the form y = kx with k = -1 and goes through the origin.
- B) y = -5x + 8 is not proportional because it has a y-intercept of 8 (b ≠ 0).
- C) y = -5 - 5x is not proportional because it has a y-intercept of -5 (b ≠ 0).
- D) y = x + 1 is not proportional because it has a y-intercept of 1 (b ≠ 0).
Therefore, the equation that represents a proportional relationship is A) y = -x.