Given: perpendicular distance from orgin is 5 units, and the slope is -1

To find : the equation of the line

Formula used :

We know that the perpendicular distance from a point (x_0,y₀) to the line ax + by + c = 0 is given by

The equation of a straight line is given by y=mx+c where m denotes the slope of the line.

The equation of the line is mx – y + c =0

Here x₀ = 0 and y₀= 0 , a = m , b = -y , c = c and D=5 units

D

Slope of the line = m = -1 ,Substituting in the above equation we get,

Thus the equation of the straight line is y = x + 5 or x + y - 5 = 0