Find the equation of the line which intercepts a length 2 on the positive direction of x-axis and is inclined at 135 with the positive direction of y axis.

Since the required line makes an angle 135 degrees with the positive direction of y-axis, it makes 45 degrees with the positive direction of x-axis.

 

Slope =

 

Also the required makes an intercept of 2 units on the positive direction of x-axis.

 

Thus, the required line passes through the point (2, 0)

 

Equation of the line with slope 'm' and passing through the point (x1, y1) is

 

y - y1 =m(x - x1)

 

That is, the equation of the line with slope 1 and passing through the point (2, 0) is

 

y - 0 = 1 (x - 2)

 

That is the required equation is y = x - 2