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 statements must be true of a graph showing the relationship between them:

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.

Let's break it down:

- **C**: When one quantity increases, the other also increases, which generally leads to the graph rising from left to right.

- **D**: Proportional relationships are linear, meaning they form a straight line when graphed.

- **E**: A proportional relationship that passes through the origin means that if one quantity is zero, the other will also be zero (i.e., \(y = kx\) where \(k\) is a constant).

- **F**: Proportionality means all points on the graph represent equivalent ratios of the two quantities.

**A** (The graph is a curve) is false for a proportional relationship since it is linear.
**B** (The points on the graph are connected) is not necessarily true for discrete data points, though the relationship is still linear.