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
C
C
B
B
A
A
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The graph that shows a proportional relationship is Graph B.
The graph that shows a proportional relationship is graph A.
To answer the question, you need to understand what a proportional relationship means. In a proportional relationship, as one variable increases, the other variable also increases, but at a constant rate. This means that the graph of a proportional relationship will be a straight line passing through the origin.
Looking at the given graphs, we can eliminate graphs A and C since they do not show a straight line passing through the origin.
Now we are left with graphs B and D. To determine which graph shows a proportional relationship, we need to check if the slope is constant for these graphs.
Graph B has a positive slope, but it is not a straight line. The slope changes as we move along the graph, so it does not represent a proportional relationship.
Graph D, on the other hand, is a straight line with a unit slope (slope = 1). This means that for every change in the x-value, the corresponding y-value changes by the same amount. This represents a proportional relationship.
Therefore, the graph that shows a proportional relationship is graph D.