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Question
Answer the following question:
Which of the following lines passes through the origin?
Options
x = 2
y = 3
y = x + 2
2x – y = 0
Solution
2x – y = 0
Explanation:
If the line ax + by + c = 0 passes through the origin, then c = 0.
1. The equation of line is
x = 2, i.e., 1x + 0y − 2 = 0
Comparing this with ax + by + c = 0, we get,
c = −2 ≠ 0
2. The equation of line is
y = 3, i.e., 0x + 1y − 3 = 0
Comparing this with ax + by + c = 0, we get,
c = −3 ≠ 0
3. The equation of line is
y = x + 2, i.e., x − y + 2 = 0
Comparing this with ax + by + c = 0, we get,
c = 2 ≠ 0
4. The equation of line is
2x – y = 0, i.e., 2x – y + 0 = 0
Comparing this with ax + by + c = 0, we get,
c = 0
Hence, the line 2x – y = 0 passes through the origin.
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