In the given fig. (i), the solutions of the equation are (−1,1),(0,0) and (1,−1).∴ the equation which satisfies these solutions is the correct equation.Equation (ii) x+y=0, satisfies these solutions.Proof:If we put  the value of  x=−1 and y=1 in the equation x+y=0=x+y=−1+1=0∴L.H.S=R.H.Sif we put the the value of  x = 0 and y = 0=x+y=0+0=0∴L.H.S=R.H.SIf we put the value of  x=1 and y=−1=x+y=1+(−1)=1–1=0L.H.S=R.H.SHence, option (ii) x+y=0 is correct.In the given Fig.(ii) the solutions of the equation are (−1,3),(0,2) and (2,0).∴The equation which satisfies these solutions is the correct equation.Equation (iii) y=−x+2 , satisfies these solutions.Proof:If we put  the value of  x=−1 and y=3 in the equation y=−x+2y=−x +23=−(−1)+23=3∴L.H.S=R.H.Sif we put the the value of  x=0 and y=2y=−x+22=−0+22=2∴L.H.S=R.H.SIf we put the value of  x=2 and y=0y=−x+20=−2+20=0L.H.S=R.H.SHence, option (iii) y=−x+2 is correct.