If there are six values of S for one value of I, and if there are also six values of S for a second value of I, then you should be able to graph two straight lines, each with its own value of the slope and intercept. If you have velocity versus substrate data for the uninhibited enzyme, then you actually have a third concentration of I, namely I = 0, and this provides a third straight line. Can you reproduce here the form of the equation you are using?

Do you know the difference between competitive, uncompetitive, and noncompetitive inhibitions? Your Michaelis-Menton equation could be taken to mean that the inhibitor is of one of these three types, but that inference is not certain (the values of alpha and alpha' will nail it down). With respect to the question of how to find alpha and alpha', there are a couple of possibilities. Are you expected to do this with the aid of graph paper, a calculator, or a statistics program such as ProStat?