Question

Which of the following are valid reasons for why the unit rate and slope of a proportional relationship are related to each other? Select all that apply.

A) Both describe the rate at which the quantity y is increasing.
B) Both describe the change in x when y increases by 1.
C) Both values can be determined by examining the value of the y-coordinate when x = 1 on the graph.
D) Both describe the change in y when x increases by 1.
E) Both can be determined by the ratio y/x for any ordered pair.
F) Both values can be determined by examining the value of the x-coordinate when y=1 on the graph.

Answer 1

The valid reasons for why the unit rate and slope of a proportional relationship are related to each other are:

B) Both describe the change in x when y increases by 1.
C) Both values can be determined by examining the value of the y-coordinate when x = 1 on the graph.
E) Both can be determined by the ratio y/x for any ordered pair.
F) Both values can be determined by examining the value of the x-coordinate when y = 1 on the graph.

These reasons explain the relationship between unit rate and slope in a proportional relationship. Reason A is not a valid reason for the relationship between the unit rate and slope in a proportional relationship because it describes the rate at which the quantity y is increasing, which is related to the concept of rate but not directly linked to the concept of slope. The relationship between unit rate and slope is more about how changes in x and y are related in a proportional manner.