Equation of a line passing through origin is (a) x + y = 1
(b) x = 2y – 4
(c) x + y = 0
(d) y = x – 1
Answers
Equation of a line passing through origin is
(a) x + y = 1
(b) x = 2y – 4
(c) x + y = 0
(d) y = x – 1
___________________________
For equation x + y = 1 (a)
~ Let us put x as 0 first in (a)
→ x + y = 1
→ 0 + y = 1
→ y = 1
- Henceforth, coordinates (0,1)
~ Now let's put y as 0 in (a)
→ x + y = 1
→ x + 0 = 1
→ x = 1
- Henceforth, coordinates (1,0)
Refer to attachment first!
___________________________
For equation x = 2y – 4 (b)
~ Let us put x as 0 first in (b)
→ x = 2y - 4
→ 0 = 2y - 4
→ 0 + 4 = 2y
→ 4 = 2y
→ 4/2 = y
→ y = 2
- Henceforth, coordinates (0,2)
~ Now let us put y as 0 in (b)
→ x = 2y - 4
→ x = 2(0) - 4
→ x = 0 - 4
→ x = -4
- Henceforth, coordinates (-4,0)
Refer to attachment second!
___________________________
For equation x + y = 0 (c)
~ Firstly let us put x as 0!
→ x + y = 0
→ 0 + y = 0
→ y = 0
- Henceforth, coordinates (0,0)
~ Now let us put y as 0!
→ x + y = 0
→ x + 0 = 0
→ x = 0
- Henceforth, coordinates (0,0)
Refer to attachment third!
___________________________
For equation y = x – 1 (d)
~ Put x as 0 in equation!
→ y = x - 1
→ y = 0 - 1
→ y = -1
- Henceforth, coordinates (0,-1)
~ Now put y as 0!
→ y = x - 1
→ 0 = x - 1
→ 0 + 1 = x
→ x = 1
- Henceforth, coordinates (1,0)
Refer to attachment fourth!
- According to the graphs we are able to see that equation (c) that is x + y = 0 passes through origin.
Given : Equation of lines
To Find : Equation of a line passing through origin
(a) x+y =1
(b) x=2y-4
(c) x+y=0
(d) y=x-1
Solution:
Equation of a line passing through origin
Origin ( 0 , 0)
Hence origin will satisfy the equation if line passes through origin
(a) x+y =1
0 + 0 = 1
=> 0 = 1
which is not true
(b) x=2y-4
0 = 2(0) - 4
=> 0 = -4
which is not true
(c) x+y=0
0 + 0 = 0
=> 0 = 0
TRUE
Hence x+y=0 is Equation of a line passing through origin
(d) y=x-1
0 = 0 - 1
0 = -1
which is not true
Hence correct answer is x+y=0
learn More
Find the point of intersection of the line joining points (3,7) (2, -4) arn ...
brainly.in/question/13398071
(i) Draw the graphs of 2x + y = 6 and y = 2x + 2 intersecting Xand Y ...
brainly.in/question/14686813
Use graph paper for this question. Draw the graph of 3x - 2y + 4 = 0 ...
brainly.in/question/15383620