The equation of a line is `x - y = 4`. Find its slope and y-intercept. Also, find its inclination. 

Answer

To solve the problem, we need to find the slope, y-intercept, and inclination of the line given by the equation \( x - y = 4 \).

### Step 1: Rewrite the equation in slope-intercept form
The slope-intercept form of a line is given by the equation:
\[ y = mx + c \]
where \( m \) is the slope and \( c \) is the y-intercept. We start with the given equation:
\[ x - y = 4 \]
To convert it to slope-intercept form, we can isolate \( y \):
\[ -y = -x + 4 \]
Now, multiply through by -1:
\[ y = x - 4 \]

### Step 2: Identify the slope and y-intercept
Now that we have the equation in the form \( y = mx + c \):
- The slope \( m \) is the coefficient of \( x \), which is \( 1 \).
- The y-intercept \( c \) is the constant term, which is \( -4 \).

Thus, we have:
- Slope \( m = 1 \)
- Y-intercept \( c = -4 \)

### Step 3: Find the inclination of the line
The inclination \( \theta \) of a line is given by the formula:
\[ \theta = \tan^{-1}(m) \]
Substituting the slope we found:
\[ \theta = \tan^{-1}(1) \]
We know that:
\[ \tan^{-1}(1) = 45^\circ \]

### Final Answers
- Slope: \( 1 \)
- Y-intercept: \( -4 \)
- Inclination: \( 45^\circ \)

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