Question
Use the image to answer the question.
A graph with x and y axes shows four curves labeled A, B, C, and D. Curve A has a step-like structure initiating at the origin, increasing steadily, tapering to a point, and again increasing. Curve B begins at the origin and is an increasing concave down curve. Curve C is a straight line with a unit slope. Curve D is a straight line that initiates at a point on the y-axis and then increases steadily.
Identify the proportional relationship from the graph.
(1 point)
Responses
Graph D
Graph D
Graph B
Graph B
Graph A
Graph A
Graph C
Graph C
The proportional relationship can be identified from the graph as Curve D.
To identify the proportional relationship from the graph, we need to analyze the behavior of the curves.
Graph D is a straight line that increases steadily. This indicates a linear relationship, where as the x-values increase, the y-values also increase at a constant rate. Therefore, Graph D represents a proportional relationship.
Graph B is an increasing concave down curve. This suggests a nonlinear relationship, as the rate of increase is not constant. Therefore, Graph B does not represent a proportional relationship.
Graph A has a step-like structure that increases, tapers, and then increases again. This irregular behavior contradicts a proportional relationship, as there are sudden changes in the rate of increase. Thus, Graph A does not represent a proportional relationship.
Graph C is a straight line with a unit slope. This indicates a linear relationship, where the y-values increase by the same amount as the x-values increase. Therefore, Graph C represents a proportional relationship.
Based on this analysis, the correct answer is Graphs D and C, as they both represent proportional relationships.