yes, a graph of a direct variation must pass through the origin because direct variation is always in form of y=mx where x and y are variables and m is a constant.
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For a direct variation, y=kx where k is the constant of variation if x =0 then y=0 and the graph of y=kx passes through the origin. -Indiana Prentice Hall Algebra 2 Text Book.
The formula direct variation is xk=y, where k is the constant of variation.Direct variation functions always pass through the origin. Direct variation functions are linear functions (goes in a straight line), except that they pass through the origin. Regular linear functions don't pass through the origin. That is the only difference.
The graph must be linear and pass thru the origin
It represents a direct proportion and whose graph is a straight line through the origin.
Direct proportionality. Their graph would be a straight line through the origin, with the slope equal to the ratio.