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

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### 2 Answers

The equation of any line making angle of 135 degree with x axis is given by: y ={ tan(135degree)})x+c. Or

y = -x+c, as tan135 = -1.

Now the above line passes through (- , 2). So (-1,2) should satisfy y= -x+c. So bstitute (-1, 2) in the equation:

-1 = -1 + c. Or c = -1+1 = 0.

So, c = 0.

Therefore , the equation y= -x+c, with c = 0, becomes:

y = -x+0 We can write this in the form x+y = 0 , aline passing through the origin.

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**