Find the equations of the lines passing through point (-2, 0) and equally inclined to the co-ordinate axes.

Answer

To find the equations of the lines passing through the point (-2, 0) and equally inclined to the coordinate axes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the equations of lines that pass through the point (-2, 0) and are equally inclined to the coordinate axes. Lines that are equally inclined to the axes have slopes of 1 or -1.

2. **Using the Slope-Intercept Form**: The general equation of a line in slope-intercept form is given by:
\[ y = mx + c \]
where \( m \) is the slope and \( c \) is the y-intercept.

3. **Finding the Equations for Slope 1**: For a line with a slope of 1, the equation can be written as:
\[ y = x + c \]
Since the line passes through the point (-2, 0), we can substitute these coordinates into the equation to find \( c \):
\[ 0 = -2 + c \implies c = 2 \]
Therefore, the equation of the line with slope 1 is:
\[ y = x + 2 \]

4. **Finding the Equations for Slope -1**: For a line with a slope of -1, the equation can be written as:
\[ y = -x + c \]
Again, substituting the point (-2, 0):
\[ 0 = -(-2) + c \implies c = -2 \]
Therefore, the equation of the line with slope -1 is:
\[ y = -x - 2 \]

5. **Writing the Final Equations**: We can express both equations in standard form:
- For the line with slope 1:
\[ y - x - 2 = 0 \implies x - y + 2 = 0 \]
- For the line with slope -1:
\[ y + x + 2 = 0 \]

### Final Answer:
The equations of the lines passing through the point (-2, 0) and equally inclined to the coordinate axes are:
1. \( x - y + 2 = 0 \)
2. \( x + y + 2 = 0 \)