Equations of the Expected Value Lines

Supposing that the probabilities of state #1 and state #2 are *p*_{1}, *p*_{2}, the expected value of payoff for the *i*-th alternative is

v_{i1}(1-p_{2}) + v_{i2}p_{2} = v_{i1} – v_{i1}p_{2} + v_{i2}p_{2} = v_{i1} + (v_{i2}-v_{i1})p_{2}

The last expression represents a line that connects points *v _{i1}* on the left axis and