Final answer:
Option 4, y = -2/5x - 5, represents a function with the same rate of change as y = -2/5x - 2, because both functions share the same slope of -2/5.
Step-by-step explanation:
The relationship that represents a function with the same rate of change as the function y = -2/5x - 2 is option 4) y = -2/5x - 5. The rate of change of a function in a linear equation of the form y = mx + b is represented by the coefficient of x, which is m. This is referred to as the slope of the line.
In this case, the original function has a slope of -2/5. For another function to have the same rate of change, its slope must also be -2/5. Option 4 has this slope, while the other options either have different slopes or different signs, which would indicate a different rate of change.