What is the slope of the line whose inclination is :
`(i) 0^(@)` `(ii) 60^(@)` `(iii) 150^(@)` ?

Answer

To find the slope of the line given its inclination, we can use the formula:

\[ m = \tan(\theta) \]

where \( m \) is the slope and \( \theta \) is the angle of inclination.

Let's solve the problem step by step for each given inclination.

### Step 1: For \( \theta = 0^\circ \)

1. **Substitute the value of \( \theta \)**:
\[ m = \tan(0^\circ) \]

2. **Calculate \( \tan(0^\circ) \)**:
\[ \tan(0^\circ) = 0 \]

3. **Conclusion**:
\[ m = 0 \]

### Step 2: For \( \theta = 60^\circ \)

1. **Substitute the value of \( \theta \)**:
\[ m = \tan(60^\circ) \]

2. **Calculate \( \tan(60^\circ) \)**:
\[ \tan(60^\circ) = \sqrt{3} \]

3. **Conclusion**:
\[ m = \sqrt{3} \]

### Step 3: For \( \theta = 150^\circ \)

1. **Substitute the value of \( \theta \)**:
\[ m = \tan(150^\circ) \]

2. **Calculate \( \tan(150^\circ) \)**:
- We know that \( \tan(150^\circ) = \tan(180^\circ - 30^\circ) = -\tan(30^\circ) \)
- Since \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \), we have:
\[ \tan(150^\circ) = -\frac{1}{\sqrt{3}} \]

3. **Conclusion**:
\[ m = -\frac{1}{\sqrt{3}} \]

### Final Results

- For \( \theta = 0^\circ \), the slope \( m = 0 \)
- For \( \theta = 60^\circ \), the slope \( m = \sqrt{3} \)
- For \( \theta = 150^\circ \), the slope \( m = -\frac{1}{\sqrt{3}} \)