Given:
The line makes an angle of 30° with the positive direction of the y-axis, measured anticlockwise.
Step 1: Convert the angle to the angle with the x-axis
The positive y-axis is 90° from the positive x-axis.
So, angle made by the line with the positive x-axis =
90° + 30° = 120°
Step 2: Use the formula for slope
Slope of a line making an angle θ with the positive x-axis is:
m = tan θ
Here, θ = 120°
Step 3: Evaluate tan 120°
tan 120° = tan(180° − 60°)
tan 120° = −tan 60° = −√3
Final Answer:
The slope of the required line is
−√3