If two quantities are proportional, which must be true of a graph showing the relationship between them? Select all that apply.

Question

A
The graph is a curve.
B
The points on the graph are connected.
C
The graph increases from left to right.
D
The points of the graph form a straight line.
E
The points of the graph must include the origin.
F
The points must all form equivalent ratios.

Answer 1

If two quantities are proportional, the following must be true of a graph showing the relationship between them:

C. The graph increases from left to right.
This is true if we consider positive values; as one quantity increases, the other quantity also increases.

D. The points of the graph form a straight line.
This is true for proportional relationships, as they represent a constant ratio between the two quantities.

E. The points of the graph must include the origin.
This is true because, in a proportional relationship, when one quantity is zero, the other quantity must also be zero, hence the graph passes through (0,0).

F. The points must all form equivalent ratios.
This is true as proportions represent equivalent ratios between two quantities.

So, the correct answers are C, D, E, and F.

A is incorrect because a proportional relationship is represented by a straight line, not a curve. B is not a necessary condition since the points do not need to be connected if we are considering discrete points.