Use the image to answer the question.

Question

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.

Decide which graph shows a proportional relationship.

(1 point)
Responses

C
C

A
A

D
D

B
B
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Answer 1

A proportional relationship is characterized by a constant ratio between two quantities, which is represented graphically as a straight line that passes through the origin (0,0) with a slope (which may be positive or negative but does not necessarily need to be constant).

Based on the descriptions you provided:

• Graph A has a negative slope but does not pass through the origin (indicating a negative relationship).
• Graph B has a positive slope but does not pass through the origin (indicating it does not represent a proportional relationship).
• Graph C is an increasing concave up curve starting at the origin, which suggests a non-linear relationship.
• Graph D is a straight line with a unit slope that passes through the origin.

Therefore, the graph that shows a proportional relationship is:

D