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
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