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From the choices given below, choose the equation whose graphs are given in Fig. (i) y = x + 2 (ii) y = x – 2 (iii) y = –x + 2 (iv) x + 2y = 6

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From the choices given below, choose the equation whose graphs are given in Fig.

(i) y = x + 2

(ii) y = x – 2

(iii) y = –x + 2

(iv) x + 2y = 6

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The points given in the figure are (0,2), (2,0), (-1, 3)

Substituting the values for x and y from these points in the equations, we get,

(i) y = x + 2

(0, 2) ⟹ 2 = 0 + 2

2 = 2

(2, 0) ⟹ 0 = 2+2

0 ≠ 4 ........ equation not satisfied

(-1, 3) ⟹ 3 = -1 + 2

3 ≠ 1 ........... equation not satisfied

(ii) y = x – 2

(0,2) ⟹ 2 = 0 – 2

2 ≠ -2 ........... equation not satisfied

(2, 0) ⟹ 0 = 2–2

0= 0

(-1, 3) ⟹ 3 = –1 – 2

3 ≠ –3 ........... equation not satisfied

(iii) y = –x + 2

(0,2) ⟹ 2 = -0 + 2

2 = 2

(2, 0) ⟹ 0 = -2 + 2

0 = 0

(-1, 3) ⟹ 3 = -(-1)+2

3 = 3

(iv) x + 2y = 6

(0,2) ⟹ 0 + (2 × 2) = 6

4 ≠ 6 .......... equation not satisfied

(2, 0) ⟹ 2 + (2 × 0) = 6

2 ≠ 6 ............ equation not satisfied

(-1, 3) ⟹ -1 + (2 × 3) = 6

5 ≠ 6 ........... equation not satisfied

Since, only equation y = –x + 2 satisfies all the points, the equation whose graphs are given in Figure is y = –x+2

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