Write the equation of the line passing through the point (-1;2) and making an angle of 135 with the axis of x.

We'll write the equation of the line that passes through a
given point and it makes an angle with the axis of X.

(y -
y1) = m (x - x1)

We know that m = tan a, where a is the
angle made by the line with the axis of X.

m = tan
135

We'll substitute the coordinates of the point into the
equation:

y - 2 = tan 135(x +
1)

We'll write tan 135 = tan (180 -
45)

tan (180 - 45) = (tan 180 - tan 45)/(1 + tan
180*tan45)

tan (180 - 45) = (0 -
1)/(1+0*1)

tan (180 - 45) =
-1

tan 135 = tan (180 - 45) =
-1

the equation of the line
is:

y - 2 = -1*(x + 1)

We'll
remove the brackets:

y - 2 = -x -
1

We'll add x + 1 both
sides:

y + x - 2 + 1 = 0

We'll
combine like terms:

x + y - 1 =
0

The equation of the line that passes
through the point (-1,2) and makes an angle of 135 degrees with the axis of X
is:

x + y - 1 =
0