y = 2x + 4 is linear -- any equation involving only first powers of x and y (and constants) is linear. You'll usually see linear equations in the forms y = mx + b, ax + by = c, or y - y1 = m(x - x1).
If you take any two points, find the slope of the line between them, and then plug in one point to solve for the constant term (like you did), you will get a linear equation through those points.
