Direct variation means that a linear function can be written as y = kx.
The y-intercept must be (0, 0).
The constant, k, is the slope.
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Linear has a slope direct does not but both go through the orgin
if the line runs through the origin it is a direct variation no matter if it is increasing or decreasing
Y=1/x
You then have a linear relationship, or a direct variation. A straight line through the origin.
Assuming the domain is unbounded, the linear function continues to be a linear function to its end.