Question

(Will give Brainliest) Which graph represents a function with direct variation?

Answer 1

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:

1. It is a straight line: because the slope is the ratio y/x = k
2. 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.

Answer 2

A graph that would represent a direct variation would be that graph that is sloping upward to the right. A direct variation means that as one variable increases, the other variable increases as well. So, in a graph it should be directed to the right and each data is increasing up.