Theory:

The construction of a line parallel to the given line can be done using a ruler and a compass only.
 
Step 1: Draw a line \(x\) and take a point \(P\) outside the line.
 
1.PNG
 
Step 2: Take any point \(Q\) on line \(x\) and draw a line joining \(P\) and \(Q\).
 
2.PNG
 
Step 3: With \(Q\) as the centre, and take any radius, draw an arc cutting the line \(x\) at \(R\) and \(PQ\)  at \(S\).
 
3.PNG
 
Step 4: With \(P\) as the centre and with the same radius, draw an arc \(TU\) cutting \(PQ\) at \(V\).
 
4.PNG
 
Step 5: Measure the radius of \(RS\) by placing the pointed tip of the compass at \(R\) and the pencil at \(S\). With the same measure of radius and with \(V\) as the centre, draw an arc cutting the arc \(TU\) at \(W\).
 
5.PNG
 
Step 6: Join \(PW\) and draw a line \(y\).
 
6.PNG
 
From the diagram, we can see that \(\angle PQR\) and \(\angle WPQ\) are alternate interior angles.
 
Therefore, the lines \(x\) and \(y\) are parallel.