Graphs of Proportional Relationships Quick Check
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Question
Use the image to answer the 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
D
D
A
A
B
B
C
The correct answer is D.
The correct answer is D.
Graph D shows a straight line with a unit slope. This indicates that the relationship between the x and y values is proportional.
To determine which graph shows a proportional relationship, we need to understand what a proportional relationship is. In a proportional relationship, the ratio between the y-values and the x-values remains constant. In other words, as the x-values increase or decrease, the y-values also increase or decrease by the same ratio.
Let's analyze each graph to see if it exhibits a proportional relationship:
Graph A: This graph shows a straight line with a negative slope and intercepts on both the x and y axes. It does not exhibit a proportional relationship because the ratio between the y-values and x-values is not constant.
Graph B: This graph shows a straight line with a positive slope and a y-intercept above the origin. Similar to Graph A, it does not exhibit a proportional relationship since the ratio between the y-values and x-values is not constant.
Graph C: This graph shows an increasing concave-up curve that originates at the origin. While it does exhibit a relationship between the x and y-values, it is not a proportional relationship because the ratio between the y-values and x-values is not constant.
Graph D: This graph shows a straight line with a unit slope. A slope of 1 indicates that for every increase of 1 in the x-values, there is a corresponding increase of 1 in the y-values. This exhibits a proportional relationship because the ratio between the y-values and x-values remains constant.
Therefore, the correct answer is D, as Graph D shows a proportional relationship.