> How did they explain what plotting was without defining a line?

Plotting is simply putting a point for a specific value. Drawing the line is inferring the un-plotted points from the plotted ones which may or may not be correct though for y = x - 3, it's easy enough to prove that a straight line covers all the solutions.

If "plotting" is only defined in terms of lines, then a student could attempt to plot y = x ^ 2 using only two points and a straight line.