Recognize that every proportional relationship graphs as a straight line through the origin, and read the constant of proportionality as the line's steepness.
Graph a proportional relationship y = kx and something clean happens: the line always passes through the point (0, 0), the origin. That makes sense -- if x is 0 (zero pounds, zero hours, zero of anything), y must also be 0.
The line's steepness IS the constant of proportionality. In fact, the point (1, k) is always on the line, since y = k x 1 = k. So you can read k straight off the graph by finding the height of the line at x = 1.
Mastery looks like: They identify k from a graph using the point (1, k) or any point's ratio, and explain why non-origin lines are not proportional.
Common stumbles: Assuming any straight line is automatically proportional, without checking that it passes through the origin.