Sample A
Rate of change, slope and constant are all related.  They are so, because they are the same thing.  They all allow you to see the relationship between two quantities that are changing.

Sample B
The rate of change allows you to see the relationship between two quantities that are changing.  The rate of change can also be called a slope.  The constant of variation is the constant in a direct variation.

Sample C
The rate of change allows you to see the relationship between two quantities that are changing and you graph it on a slope.  Then the way you graph it is linear and the function for the linear equation is called linear equation.  And the rate of change is the constant variation.

Sample D
Rate of change allows you to see the relationship between two quantities that are changing.  The equation for the rate of change is rate of change equals change in dependent variable divided by change in independent variable.  Slope is the measure of the steepness of a line.  The ratio of the vertical change to the horizontal change, and constant of variation is the constant k in a direct variation.  The equation for finding slope is slope equals vertical change divided by horizontal change, as long as the difference in the x values is not equal to zero.

Teacher Comments
This question was designed to stimulate critical thinking.  All three concepts had been presented individually and practiced for several days.  I had hoped that the students would recognize the similarity of purpose in the three concepts and that all represented rates of change that when graphed produced the slope or steepness of the line graphed.  Most of the students were able to define or identify the individual processes.  Example A had recognized the fact that all three are indeed the same concept applied to different situations; B and C are less articulate, but show some recognition of the relationship; D only stated a definition for each process, but did not seem to recognize any relationship.  I was pleased that the majority of students were recognizing and linking the processes, but I saw very little actual comparison and contrast of the three in any responses.  The social studies teacher had also noticed this lack, leading to some team teaching on what comparison and contrast looked like and application of the process across the curriculum.