Equations of the Expected Value Lines

Supposing that the probabilities of state #1 and state #2 are p1, p2, the expected value of payoff for the i-th alternative is

vi1(1-p2) + vi2p2 = vi1 vi1p2 + vi2p2 = vi1 + (vi2-vi1)p2

The last expression represents a line that connects points vi1 on the left axis and vi2 on the right axis (see Picture 2.3).