A direct variation must satisfy both of two conditions: 1. It must pass through the origin (which this graph does) 2. It must be a straight line (which this graph does not satisfy). Therefore the given graph is NOT a direct variation.
Corollary: If a function satisfies both of the above conditions, it has an equation of the form y=kx where k is a constant not equal to zero.
This way, we can tell a direct variation even from an equation. Note: y=4x+2 is NOT a direct variation because the "+2" makes the straight line not pass through the origin. y=2x^2 is not a direct variation because a function containing any other power of x is no longer a straight line.
