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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

D
D

A
A

B

1 answer

A proportional relationship is characterized by a straight line that passes through the origin (0,0) and has a constant rate of change. Among the graphs described:

  • Graph A shows a straight line with a negative slope, which does not indicate a proportional relationship since it does not pass through the origin in a positive manner.
  • Graph B shows a straight line with a positive slope but has a y-intercept above the origin, which means it is not proportional.
  • Graph C shows an increasing concave up curve initiating at the origin, which typically indicates a nonlinear relationship, not a proportional one.
  • Graph D shows a straight line with a unit slope, indicating a consistent linear relationship that also passes through the origin.

Therefore, the graph that shows a proportional relationship is:

D