1. **Problem statement:** Find the slope of a line that makes a 30° angle with the positive direction of the y-axis measured anticlockwise. 2. **Understanding the problem:** The slope of a line is defined as the tangent of the angle it makes with the positive x-axis. 3. **Key formula:** If $\theta$ is the angle between the line and the positive x-axis, then the slope $m$ is given by: $$m = \tan(\theta)$$ 4. **Given:** The line makes a 30° angle with the positive y-axis anticlockwise. 5. **Find the angle with the positive x-axis:** - The positive y-axis is at 90° from the positive x-axis. - Since the line is 30° anticlockwise from the positive y-axis, the angle with the positive x-axis is: $$\theta = 90^\circ + 30^\circ = 120^\circ$$ 6. **Calculate the slope:** $$m = \tan(120^\circ)$$ 7. **Evaluate $\tan(120^\circ)$:** - $120^\circ = 180^\circ - 60^\circ$ - Using the identity $\tan(180^\circ - x) = -\tan(x)$: $$\tan(120^\circ) = -\tan(60^\circ) = -\sqrt{3}$$ 8. **Final answer:** The slope of the line is: $$m = -\sqrt{3}$$