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
B
B
D
D
C
C
A
A
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The correct answer is A. Graph A shows a straight line with a negative slope that intersects both the x and y axes. This indicates a proportional relationship, where as x increases, y decreases in a consistent ratio.
The correct answer is A. Graph A shows a straight line with a negative slope and both x and y intercepts, indicating a proportional relationship.
To determine which graph represents a proportional relationship, we need to understand the concept of proportionality. In a proportional relationship, as the value on one axis increases or decreases, the value on the other axis changes at a constant rate.
Looking at the graphs, we can eliminate graphs A and C because they represent curves rather than straight lines. In a proportional relationship, the relationship between x and y is represented by a straight line.
Graph D represents a straight line with a unit slope, indicating that for each increase or decrease in x, there is an equal increase or decrease in y. This suggests a constant rate of change and a proportional relationship.
Graph B also represents a straight line, but with a positive slope. While the relationship between x and y is linear, it does not indicate a proportional relationship because the slope is not equal to 1. Therefore, graph B does not represent a proportional relationship.
Based on this analysis, the correct answer is D - Graph D represents a proportional relationship.