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From the choices given below, choose the equation whose graphs are given in Fig. (i) y = x (ii) x+y = 0 (iii) y = 2x

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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

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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.

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