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Which of the following is the correct equation of a line passing through (2, 14), and check how many lines are possible there?

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7 x − y = 0

; Infinitely many lines are possible.

x − 7 y = 0

; Only 3 lines are possible.

7 x − y = 0

; Only three lines are possible

None of the above

answer is A.

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Detailed Solution

We have been given a point (2, 14) where

x = 2

and

y = 14

.
Now, for the equation of lines passes through (2, 14), the value of the expression

7 x − y

is,

7 x − y = 7 × 2 − 14

⇒ 7 x − y = 14 − 14 ⇒ 7 x − y = 0

It can be observed that point (2, 14) satisfies the equation

7 x − y = 0.

We know that we can draw infinitely many numbers of lines through a point as shown below.
Thus, there are infinitely many lines that pass through (2, 14).
Question Image

The value of the expression

x − 7 y

is,

x − 7 y = 2 − 7 × 14 ⇒ x − 7 y = 2 − 98 ⇒ x − 7 y = − 96

⇒ x − 7 y ≠ 0

Thus,

x − 7 y = 0

is not the equation of a line that passes through (2, 14).
Hence, option (1) is correct.

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