A figure shows four graphs labeled A, B, C, and D, each with an x and y axis and 0 at the origin, and each showing a curve. Graph A shows a straight line with a negative slope having x and y intercepts. Graph B shows a straight line with a positive slope having a y intercept above origin. Graph C shows an increasing concave up curve initiating at the origin. Graph D shows a straight line with a unit slope.

Question

Decide which graph shows a proportional relationship.

(1 point)
Responses

B
B

D
D

A
A

C

Answer 1

A proportional relationship is characterized by a straight line passing through the origin (0,0) and having a constant ratio between the variables.

Based on your description:

• Graph A shows a straight line with a negative slope having x and y intercepts. This does not pass through the origin.
• Graph B shows a straight line with a positive slope having a y intercept above the origin. This also does not pass through the origin.
• Graph C shows an increasing concave up curve initiating at the origin. This suggests a nonlinear relationship, not proportional.
• Graph D shows a straight line with a unit slope. If it passes through the origin, it indicates a proportional relationship.

Thus, the graph that shows a proportional relationship is:

D.