Final answer:
A proportional relationship implies that all points will lie on a straight line that passes through the origin. By finding that the ratio of y/x for all points in the table is consistent, we determine that the graph of the relationship is a line through (0, 0) and (3.6, 14.4). Therefore correct option is A
Step-by-step explanation:
The question describes a proportional relationship between two variables, x and y. In a proportional relationship, the ratio between the two variables remains constant. This means that if you were to plot the points given in the table on a graph, they would all lie on a straight line that passes through the origin (0, 0), because the constant ratio also implies that at x=0, y must be 0 as well.
Given the set of points (3.6, 14.4), (5.9, 23.6), and (1.8, 7.2), we can calculate the ratio y/x which should be the same for all points if the relationship is indeed proportional.
For the first point (3.6, 14.4), y/x = 14.4/3.6 = 4. For the second point (5.9, 23.6), y/x = 23.6/5.9 = 4. And for the third point (1.8, 7.2), y/x = 7.2/1.8 = 4.
Since the ratio is consistent, we confirm a proportional relationship, which means the correct answer is: "A line that goes through (0, 0) and (3.6, 14.4)."