You can think of a line as a set of points (x,y) which satisfy an equation in the form of y = mx + d. Hence all the points (x,y) which satisfy that equation are on the line, all the points which don't aren't. First I'll transform this equation into the form y = mx + d, because it will be a bit nicer to use for this particular problem:
y - 3 = 5(x-9) | + 3
y = 5x - 45 + 3
y = 5x - 42
Now for example, to see if A = (3,9) is on the line, you substitute x = 3 and y = 9 into that equation and if you' get a true statement, you know it's on the line, otherwise it isn't.
9 = 5*3 - 42
9 = 15 - 42 = -27 false!
Hence A is not on the line.