Find the inclination of the line whose slope is:
1

Answer

To find the inclination of the line whose slope is 1, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Inclination**:
The inclination of a line is the angle (θ) that the line makes with the positive x-axis. The slope (m) of the line is related to this angle by the formula:
\[ m = \tan(\theta) \]

2. **Identify the Given Slope**:
In this problem, we are given that the slope (m) of the line is 1. Therefore, we can write:
\[ m = 1 \]

3. **Set Up the Equation**:
Using the relationship between slope and inclination, we can substitute the value of m into the equation:
\[ 1 = \tan(\theta) \]

4. **Find the Angle θ**:
We need to determine the angle θ for which the tangent is equal to 1. From trigonometric values, we know:
\[ \tan(45^\circ) = 1 \]
Therefore, we can conclude:
\[ \theta = 45^\circ \]

5. **State the Final Answer**:
The inclination of the line whose slope is 1 is:
\[ \theta = 45^\circ \]