From the choices given below, choose the equation whose graphs are given in Fig.
(i) y = x
(ii) x+y = 0
(iii) y = 2x
(iv) 2+3y = 7x
The points given in the figure are (0, 0), (-1,1), (1,-1)
Substituting the values for x and y from these points in the equations, we get,
(i) y = x
(0, 0) ⟹ 0 = 0
(-1, 1) ⟹ -1 ≠ 1 ....... equation not satisfied
(1, -1) ⟹ 1≠ -1 ........ equation not satisfied
(ii) x + y = 0
(0,0) ⟹ 0+0 = 0
(-1, 1) ⟹ -1 + 1 = 0
(1, -1) ⟹ 1+(-1) =0
(iii) y = 2x
(0, 0) ⟹ 0 = 2×0
0 = 0
(-1, 1) ⟹ 1 = 2×(-1)
1≠ -2 ........ equation not satisfied
(1, -1) ⟹ -1 = 2×1
-1 ≠ 2 .............. equation not satisfied
(iv) 2+3y = 7x
(0,0) ⟹ 2+(30) = 7×0
2 ≠ 0 .............. equation not satisfied
(-1, 1)
⟹ 2 + (3 × 1) = 7×-1
5 ≠ -7 ........... equation not satisfied
(1, -1) ⟹ 2+(3×-1) = 7×1
-1 ≠ 7 ........... equation not satisfied
Since, only equation x + y = 0 satisfies all the points.