A motor cyclist is moving along the line `x – y = 2` and another motor cyclist is moving along the line `x – y = 4` find out their moving direction.

Answer

To solve the problem of determining the moving direction of two motorcyclists moving along the lines \( x - y = 2 \) and \( x - y = 4 \), we can follow these steps:

### Step 1: Understand the equations of the lines
The equations given are:
1. \( x - y = 2 \)
2. \( x - y = 4 \)

These equations represent straight lines in a two-dimensional coordinate system.

### Step 2: Rearrange the equations
We can rearrange both equations into the slope-intercept form \( y = mx + b \) to identify their slopes.

For the first equation:
\[ x - y = 2 \implies y = x - 2 \]
The slope \( m_1 = 1 \).

For the second equation:
\[ x - y = 4 \implies y = x - 4 \]
The slope \( m_2 = 1 \).

### Step 3: Analyze the slopes
Both lines have the same slope \( m_1 = m_2 = 1 \). This indicates that the lines are parallel.

### Step 4: Determine the direction of movement
Since the lines are parallel and have the same slope, the motorcyclists are moving in the same direction.

### Conclusion
The two motorcyclists are moving in the same direction along their respective paths defined by the lines \( x - y = 2 \) and \( x - y = 4 \).

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