From the choices given below, choose the equation whose graphs are given in Fig. (i) and Fig. (ii). For fig. (i) (i)y=x (ii)x+y=0 (iii)y=2x (iv)2+3y=7x For fig. (ii) (i)y=x+2 (ii)y=x (iii)y=-x+2 (iv)x+2y=6

In the given fig. (i), the solutions of the equation are (−1,1),(0,0)and(1,−1). Therefore, 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 Therefore, L.H.S=R.H.S If we put the the value of x = 0 and y = 0 = x+y=0+0=0 Therefore, L.H.S=R.H.S If we put the value of x=1 and y=−1 = x+y=1+(−1)=1−1=0 L.H.S=R.H.S Hence, 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). Therefore, 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+2 y=−x+2 3=−(−1)+2 3=3 Therefore, L.H.S=R.H.S If we put the the value of x=0 and y=2 y=−x+2 2=−0+2 2=2 Therefore, L.H.S=R.H.S If we put the value of x=2 and y=0 y=−x+2 0=−2+2 0=0 L.H.S=R.H.S Hence, option (iii) y=−x+2 is correct.