Graphs of Proportional Relationships Quick Check
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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 A
Graph A
Graph B
Graph B
Graph C
To identify the proportional relationship from the graph, we need to determine which curve represents a consistent rate of change between the x and y variables. A proportional relationship is one in which the ratio of y to x is constant.
Looking at the descriptions of the curves, we can rule out several options:
- Curve A has a "step-like structure," which implies that it jumps in intervals and does not maintain a consistent ratio between x and y.
- Curve B is an "increasing concave down curve," which suggests that it represents a relationship that is changing, but not a constant one, as the concave motion indicates that the rate of increase is decreasing.
- Curve C is a "straight line with a unit slope," which implies that it's a linear relationship where the change in y is directly proportional to the change in x, maintaining a constant rate (ratio of y to x is constant). This characteristic defines a proportional relationship.
- Curve D is a "straight line that initiates at a point on the y-axis," which implies that it does not start at the origin (0,0). This kind of graph usually represents a linear relationship but not a proportional one because there's an intercept that does not allow the ratio of y to x to remain constant for all values of x (in a proportional relationship, when x is 0, y has to be 0 as well).
Given these considerations, the correct answer is:
Graph C
It's important to note that a graph representing a proportional relationship will always be a straight line that passes through the origin (0,0) because this indicates that y is always some constant multiple (the proportionality constant) of x.