Question

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