The graph represents a proportional relationship as it is a straight line passing through the origin. Therefore, the correct answer is (b) Yes, it is a proportional relationship because the graph is a straight line.
The graph in question depicts the relationship between the number of cars (x-axis) and the corresponding number of wheels (y-axis). To determine whether the relationship is proportional, we need to assess key characteristics.
A proportional relationship is one where the ratio of y to x is constant. In this case, looking at the graph and the given points (0, 2), (1, 6), (2, 10), and (3, 12), we can observe that the ratio of the number of wheels to the number of cars is consistently 2:1.
Now, to address the options:
a. Yes, it is a proportional relationship because the graph goes through the origin.
This is true. In a proportional relationship, the graph passes through the origin (0, 0), indicating that when there are zero cars, there are zero wheels.
b. Yes, it is a proportional relationship because the graph is a straight line.
This is also correct. A proportional relationship is represented by a straight line passing through the origin.
c. No, it is not a proportional relationship because the graph is not a straight line.
This statement is incorrect; the graph is indeed a straight line.
d. No, it is not a proportional relationship because the graph does not go through the origin.
This is inaccurate. The graph does pass through the origin, supporting a proportional relationship.