find the equation of the line cutting off an intercept -2 from the y axis and equally inclined to the axis .

Since the required line is equally inclined with the coordinate axes, therefore, it makes either an angle of  45° or 135° with the x-axis.

So, its slop is either m =tan 45° or m = tan 135°

i.e., m  = 1 or m = -1.

It is given that c = -2.

Substituting these values in y = mx + c, we obtain the required equation of the line as:

y = 1(x) + (-2)  or y = -1(x) + (-2)

⇒ y = x - 2 or y = -x - 2