Question

Determine the equation of a line passing through (−2, 3) and making an angle of 60° with the positive direction of the X-axis.

Answer 1

Given values:

Point (x₁, y₁) = (−2, 3),

Angle of inclination (θ) = 60°

m = tan(θ)

m = tan(60°)

∴ m = `sqrt3`

Using the point–slope formula:

y − y₁ = m(x − x₁)

Substitute x₁ = −2, y₁ = 3, and m = `sqrt3`

`y - 3 = sqrt3 [x - (-2)]`

`y - 3 = sqrt3 (x + 2)`

`y - 3 = sqrt3x + 2sqrt3`

`0 = sqrt3x - y + 2sqrt3 + 3`

∴ `sqrt3x - y + 3 + 2sqrt3 = 0`

Hence, the equation of the line is `sqrt3x - y + 3 + 2sqrt3 = 0`.