Find the equation of a line whose :
y-intercept = -1 and inclination = `45^@`. 

Answer

To find the equation of a line with a given y-intercept and inclination, we can follow these steps:

### Step 1: Identify the given values
- **Y-intercept (c)** = -1
- **Inclination (θ)** = 45°

### Step 2: Calculate the slope (m)
The slope of a line can be determined using the tangent of the inclination angle:
\[ m = \tan(\theta) \]
For θ = 45°:
\[ m = \tan(45°) = 1 \]

### Step 3: Use the slope-intercept form of the equation of a line
The slope-intercept form of a line is given by:
\[ y = mx + c \]
Where:
- \( m \) is the slope
- \( c \) is the y-intercept

### Step 4: Substitute the values into the equation
Now, substituting the values of \( m \) and \( c \):
\[ y = 1 \cdot x + (-1) \]
This simplifies to:
\[ y = x - 1 \]

### Step 5: Write the final equation
Thus, the equation of the line is:
\[ y = x - 1 \]

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