Find the equation

Given: equation passes through (2,3) and make an angle of 45⁰with the line 3x + y – 5 = 0.

To find: equation of given line

Explanation:

We know that the equations of two lines passing through a point x1,y1 and making an angle α with the given line y = mx + c are

Here,
Equation of the given line is,

3x + y – 5 = 0

⇒ y = - 3x + 5

Comparing this equation with y = mx + c we get, m = - 3
x₁ = 2, y₁ = 3, α = 45∘, m = - 3.

So, the equations of the required lines are

⇒ x + 2y – 8 = 0 and 2x – y – 1 = 0

Hence, Equation of given line is x + 2y – 8 = 0 and 2x – y – 1 = 0