State the equation of the line which has the y-intercept
-5 and is equally inclined to the axes

Answer

To find the equation of the line that has a y-intercept of -5 and is equally inclined to the axes, we can follow these steps:

### Step 1: Identify the y-intercept
The y-intercept is given as -5. This means that the line crosses the y-axis at the point (0, -5).

### Step 2: Understand the inclination to the axes
A line that is equally inclined to the axes makes an angle of 45 degrees or 135 degrees with the x-axis. This means that the slope (m) of the line can be either +1 or -1.

### Step 3: Use the slope-intercept form of the equation of a line
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.

### Step 4: Write the equations for both slopes
1. For the slope \( m = 1 \):
\[ y = 1x - 5 \quad \text{(since } c = -5\text{)} \]
This simplifies to:
\[ y = x - 5 \]

2. For the slope \( m = -1 \):
\[ y = -1x - 5 \quad \text{(since } c = -5\text{)} \]
This simplifies to:
\[ y = -x - 5 \]

### Step 5: State the final equations
The equations of the lines that satisfy the given conditions are:
1. \( y = x - 5 \)
2. \( y = -x - 5 \)