The slope of a line whose inclination is `90^(@)` is .................

Answer

To find the slope of a line whose inclination is \(90^\circ\), we can use the relationship between the inclination of a line and its slope.

### Step-by-Step Solution:

1. **Understanding Inclination and Slope**:
The inclination of a line is the angle it makes with the positive x-axis. The slope (m) of a line can be calculated using the tangent of the angle of inclination (θ):
\[ m = \tan(\theta) \]

2. **Substituting the Given Angle**:
In this case, the angle of inclination is \(90^\circ\). Therefore, we substitute \(90^\circ\) into the formula:
\[ m = \tan(90^\circ) \]

3. **Calculating the Tangent**:
The tangent of \(90^\circ\) is undefined because the sine of \(90^\circ\) is 1 and the cosine of \(90^\circ\) is 0. Thus, we have:
\[ \tan(90^\circ) = \frac{\sin(90^\circ)}{\cos(90^\circ)} = \frac{1}{0} \]
Since division by zero is undefined, we conclude that:
\[ m = \text{undefined} \]

4. **Conclusion**:
Therefore, the slope of the line whose inclination is \(90^\circ\) is:
\[ \text{slope} = \text{undefined} \quad \text{or} \quad \text{slope} = \infty \]