The perpendicular distance of a line from the origin is 5 units, and its slope is - 1. Find the equation of the line.

Given: slope = - 1 and p = 5

Assuming: c be the intercept on the y - axis.

Explanation:

Then, the equation of the line is

y = - x + c [∴ m = - 1]

⇒ x + y = c

⇒

Dividing both sides by

This is the normal form of the given line.

Therefore, denotes the length of the perpendicular from the origin.

But, the length of the perpendicular is 5 units.

⇒ c =

Thus, substituting c = in y = - x + c , we get the equation of line to or