Solution:
Given, the line makes an 30° with the positive direction of y-axis measured anticlockwise.
Let the line makes an angle θ with the positive direction of x-axis.
From the above figure, we get
∠OAB = 30° (Vertically opposite angle)
In ΔAOB,
∠ABO + 30° + 90° = 180°
⇒ ∠ABO = 180° – 120° = 60°
∴ θ = 180° – ∠ABO = 180° – 60° = 120°
Slope of the line = tan120° = tan (180° – 60°) = –tan60° = -√3
Thus, the slope of the line is -√3.
