Are the two lines L1 through (-1,4) and (0,4) and L2 through (5,6) and (5,2) parallel, perpendicular or neither?

Based on fact that if 2 lines are parallel, their slopes are equal and if the 2 lines are perpendicular, the product of their slopes is -1, we'll calculate their slopes first and we'll check the relation between slopes.

To calculate the slope of the line L1, we'll use the formula:

m1 = (y2-y1)/(x2-x1)

Now, we'll substitute the coordinates:

m1 = (4-4)/(0+1)= 0/1 = 0

We'll calculate the second slope:

m2 = (2-6)/(5-5) = -4/0 = -inf. 

That means that the slope is a line which is parallel to y axis.

Since the slope m1 represents a line that is parallel to x axis, that means that the slopes are perpendicular and the lines L1 and L2 are perpendicular, too.