Final answer:
The constant of proportionality for the graph with points (0,0), (1,2), (2,4), (3,6) is found by dividing the y-coordinate by the x-coordinate for each point. The consistent ratio across all points is 2, therefore the constant of proportionality is 2. The correct answer is B.
Step-by-step explanation:
Determining the Constant of Proportionality
The question involves a graph with the points (0,0), (1,2), (2,4), and (3,6), and we are asked to find the constant of proportionality. To do this, we look for the ratio of the y-coordinate to the x-coordinate for each point, which should be consistent for all the points if they're proportional.
Starting with the second point (1,2), if we divide the y-coordinate by the x-coordinate (2 ÷ 1), we get 2. We can confirm this by checking the other points as well, for example, (2,4) which gives us 4 ÷ 2, also equaling 2. This consistency across all points indicates that the constant of proportionality is indeed 2.
The concept of proportionality is a fundamental one in mathematics, and it is particularly evident in the case of linear relationships where the ratio of y to x is constant. This is associated with a straight line that passes through the origin on a graph, which is precisely what we have in the given set of points.