Coordinate Geometry

To solve the problem, we need to find the value of such that the lines and are parallel.

1. Understanding the Condition for Parallel Lines:

Two lines are parallel if their slopes are equal.

The general form of a line is . The slope of such a line is given by:

2. Finding the Slope of the Second Line:

For the line :

,

Slope

3. Finding the Slope of the First Line:

For the line :

,

Slope

4. Setting Slopes Equal:

Since the lines are parallel:

5. Solving for :

Multiply both sides by and then solve:

Multiply both sides by 5:

Final Answer:

The value of is .