Which graph shows a proportional relationship?
A. graph AThe left-most point is at left parenthesis 1 comma 1 right parenthesis. The next point to the right is at left parenthesis 3 comma 4 right parenthesis. The next point to the right is at left parenthesis 5 comma 7 right parenthesis. The point furthest right is at left parenthesis 6 comma 8.5 right parenthesis.
B. graph BThe left-most point is at left parenthesis 1 comma 2 right parenthesis.
The next point to the right is at left parenthesis 2 comma 4 right parenthesis.
The next point to the right is at left parenthesis 4 comma 8 right parenthesis.
The point furthest right is at left parenthesis 6 comma 12 right parenthesis.
C. graph CThe left-most point is at left parenthesis 0 comma 0 right parenthesis.
The next point to the right is at left parenthesis 2 comma 5 right parenthesis.
The next point to the right is at left parenthesis 4 comma 8 right parenthesis.
The point furthest right is at left parenthesis 6 comma 10 right parenthesis.
D. graph D
Cannot be determined without a description of graph D.
Based on the given information, graph B shows a proportional relationship. Each time the x-coordinate increases by 1, the y-coordinate doubles. This indicates a constant ratio between the x and y-values, which is a characteristic of proportional relationships.
To determine which graph shows a proportional relationship, we need to look for a pattern where the ratio between the x-values and the y-values remains constant.
Let's analyze each graph:
A. In graph A, when we calculate the ratio of the y-values to the corresponding x-values, we get 4/3, 7/5, and 8.5/6, which are not equal. Therefore, graph A does not show a proportional relationship.
B. In graph B, when we calculate the ratio of the y-values to the corresponding x-values, we get 2/1, 4/2, 8/4, and 12/6. These ratios are all equal to 2. Therefore, graph B shows a proportional relationship.
C. In graph C, when we calculate the ratio of the y-values to the corresponding x-values, we get 5/2, 8/4, and 10/6. These ratios are not equal. Therefore, graph C does not show a proportional relationship.
D. The details of graph D are not provided, so we cannot determine if it shows a proportional relationship based on the information given.
Based on the analysis, graph B shows a proportional relationship, so the answer is B.