Question

Determine the equation of a line passing through (2, 2) and inclined to the X-axis at an angle of 45°.

Answer 1

Given values:

Point (x₁, y₁) = (2, 2),

Angle of inclination (θ) = 45°

m = tan(θ)

m = tan(45°)

∴ m = 1

Using the point–slope formula:

y − y₁ = m(x − x₁)

Substitute x₁ = 2, y₁ = 2, and m = 1

y − 2 = 1(x − 2)

y − 2 = x − 2

x − y − 2 + 2 = 0

∴ x − y = 0

Hence, the equation of the line is x − y = 0