Question

If the angle made by the line
with positive direction of X-axis
is 30° then slope of the line is
​

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ. The slop of a line is positive or negative according as θ is acute or obtuse. Sine a line parallel to x-axis makes an angle of 0° with x-axis, therefore its slope is tan 0° = 0.