Question

Carlos and Ethan noticed that both proportional relationships and linear functions form a straight line when graphed. Carlos claims that all linear functions are also proportional relationships. Ethan disagreed and tells Carlos that he has it backwards, that all proportional relationships are linear functions. Which statement accurately compares their observations?
A) Carlos is correct because all linear functions go through the origin.
B) Ethan is correct because all proportional relationships form a straight line and go through the origin and linear functions are linear, but they don’t all go through the origin so they are not always proportional.
C) Carlos is incorrect because no proportional relationships are linear.
D) Both Carlos and Ethan are incorrect, no proportional relationships are nonlinear.

Answer 1

Answer:

B. Ethan is correct because all proportional relationships form a straight line and go through the origin and linear functions are linear, but they don’t all go through the origin so they are not always proportional.

Step-by-step explanation:

So a proportional relationship is just a special kind of linear relationship, i.e., all proportional relationships are linear relationships (although not all linear relationships are proportional).