Direct variation: y=kx where k is some number thats not 0
that means if x is 2, y is 2k. if x is 1, y is k. if x is 0, y is 0.
notice: no matter what k is, when you put 0 in for x, y will always be 0. that means that a direct variation always goes through the origin, a.k.a. (0,0).
do all lines go through the origin? nah. a line is y=mx+b, where m and b are some numbers. a line is only a direct variation if b is 0. this makes sense because if b is 0, then the y-intercept is 0, so the line goes through the origin.
in conclusion, no, not all linear relationships are direct varations, but all direct variations are linear relationships.
