For Fig. 4. 6
(i) y = x
(ii) x + y = 0
(iii) y = 2x
(iv) 2 + 3y = 7x
Solution:
The points given in the figure 4.6 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+(3×0) = 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, the equation whose graphs are given in Fig. 4.6 is
x + y = 0
For Fig. 4. 7
(i) y = x + 2
(ii) y = x – 2
(iii) y = –x + 2
(iv) x + 2y = 6
Solution:
The points given in the figure 4.7 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 ≠ 64 --------------------------- 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 Fig. 4.7 is
y = –x + 2.
Ash Greninja 4 years, 2 months ago
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