Parallel Lines?

We can calculate the gradients (a.k.a. slopes) of each line by drawing two right angled triangles (one for each line, vertices are the endpoints of the green/purple line and the lower left corner) and dividing the length of the vertical side by the length of the horizontal side:

$m_{green} = \frac {-6}{10} = -0.6$

$m_{purple} = \frac {-5}{8} = -0.625$

Since the two gradients are not equal, therefore the green and the purple lines are not parallel.

Hence, our answer is:

$\boxed {No}$

It is simple:

Because at the beginning the difference between the line is 1 and at the end it is 2

Here is a solution without calculating the slopes. Anyone can see that the lowest points (which naturally has the same ordinate) on each line has a distance of 2. We can actually use this fact to test their parallelism of the lines by measuring the distance between any other pair of points on each line which has the same ordinate . What about the highest point in the purple line? The distance between it and its 'neighbor' (the one on the green line with the same ordinate) is obviously less than 2. Therefore they cannot be parallel.