Q: What is the slope of the line that makes an angle $30^{\circ}$ with the positive direction of the y-axis?
Answer 1:
This is the answer given in my book. Line AB makes an angle $30^{\circ}$ with the positive direction of the y-axis. So, it makes an angle $120^{\circ}$ with the positive direction of the x-axis. So, the slope of AB, $m=\tan(120^{\circ})=-\sqrt{3}$.
Answer 2:
This is the answer given by me. I agree with the answer given in my book. However, I think that the line CD also makes an angle $30^{\circ}$ with the positive direction of the y-axis. So, it makes an angle $60^{\circ}$ with the positive direction of the x-axis. So, the slope of CD, $m=\tan(60^{\circ})=\sqrt{3}$.
Isn't the answer given by me aka answer 2 also correct?
Best Answer
If it's unspecified that the slope of the line is either positive or negative ,then both the answers are absolutely correct . However , in your case , the question should have clarified the case , because it has taken the negative slope as the correct answer.