Question

Find the equation of a line through the origin that makes an angle with the positive X-axis equal to 45°.

Answer 1

If a line has inclination θ with the positive X-axis, its slope m = tan θ.

Here θ = 45°,

m = tan 45°

∴ m = 1

Equation through the origin:

The equation of a line with slope m passing through the origin (0, 0) is y = (m) x.

Substituting m = 1

y = (1) x

∴ y = x

Rewriting y = x in standard form gives x − y = 0,

Hence, the equation of a line is y = x, i.e., x − y = 0.