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

Answer 1

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.