Give the equations of two lines passing through (3, 12). How many more such lines are there, and why?

Question

Philoid · Accepted Answer

Equation of line passing through a point (a, b)

(x – a) = m(y – b)

Where ‘m’ is an integer

There are infinite lines passing through a point.

Equation of two lines passing through (3, 12)

Taking m = 1, 2

⇒ x – 3 = y – 12

⇒ x – y + 9 = 0

And, (x – 3) = 2(y – 12)

⇒ x - 3 = 2y – 24

⇒ x – 2y + 21 = 0