Question

17.

with the line x - 3y - 2 = 0.
Find the equation of lines passing through the point (1,-4) and making an angle of 135º ​

Answer 1

The equation of the line passing through the point (1,-4) and making an angle of 135º ​will be:

• 
  `y=-x-3`

Explanation:

Given the point (1, -4)

Given that the line makes an angle of 135º.

so

Slope = m = tan 135º = -1

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -1 and the point (1,-4)

`y-y_1=m\left(x-x_1\right)`

`y-\left(-4\right)=-1\cdot \left(x-1\right)`

`y+4=-\left(x-1\right)`

subtract 4 from both sides

`y+4-4=-\left(x-1\right)-4`

simplify

`y=-x-3`

Therefore, the equation of the line passing through the point (1,-4) and making an angle of 135º ​will be:

• 
  `y=-x-3`