Answer: the last picture.
Justification:
Direct variation means that the ratio of the variables is constant, i.e. y / x = k or, equivalently, y = kx.
In other words, the variables y and x vary proportionally, such that in x grow, y grows in the same proportion and quotient y/x remains constant.
That means that the graph of a function with direct variation has these features:
- It is a straight line: because the slope is the ratio y/x = k
- It passes through the origin (0,0): because y = kx = k (0) = 0.
Since the only graph that is passing through the origin (0,0) is the last graph, it is the only graph that represents a function with a direct variation.
