In Exercises, find the equation of the line which satisfy the given conditions:

Passing through and inclined with the x-axis at an angle of 75^o.

Given point = (2, 2√3) and θ = 75°

We know that m = tanθ

∴ m = tan75° = 2 + √3

We know that the point (x, y) lies on the line with slope m through the fixed point (x₀, y₀), if and only if, its coordinates satisfy the equation y – y₀ = m (x – x₀)

∴ y – 2√3 = (2 + √3) (x – 2)

⇒ y – 2√3 = (2 + √3) x + 4 – 2√3

⇒ (2 + √3) x – y + 4 – 2√3 + 2√3 = 0

⇒ (2 + √3) x – y + 4 = 0

Ans. The equation of the line is (2 + √3) x – y + 4 = 0.