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
A
A
D
D
C
C
B
B
D
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 C
Graph C
Graph A
Graph A
Graph D
Graph D
Graph B
Graph C
The graph that shows a proportional relationship is graph A.
To answer the question, we need to understand what a proportional relationship is. In a proportional relationship, the ratio between the two variables remains constant.
Looking at the given graphs, we can eliminate Graphs A, C, and D as potential options. Graph A shows a straight line, but the slope is negative, so it does not represent a proportional relationship. Graph C shows an increasing concave up curve, which means the rate of increase is changing, ruling it out as well. Graph D also shows a straight line, but with a unit slope, which means the ratio between the variables is constant, but not necessarily proportional.
This leaves us with Graph B. Graph B shows a straight line with a positive slope and a y-intercept above the origin. This suggests that as the x-variable increases, the y-variable also increases at a consistent rate. In other words, there is a proportional relationship between the variables in this graph.
Therefore, the correct answer is: B