1.
The description of set K as <span> {(x, y) | x - y = 5}, means the following:
the elements of set K are pairs (x,y)
such that: x-y=5, that is we can write(x, y) = (x, x-5).
2.
A set of (ordered) pairs is a function, if each of the first coordinates is paired to only 1 specific value, not 2 or more.
for example: {(1,2), (3, 5), (3, 8)} is not a function because 3 is not paired to only one second value, we have (3, 5) but also (3, 8).
whereas, {(-2, 4), (3, 5), (8.1, 17)} is a function, because each first coordinate is unique, we don't see it again in another pair.
3.
Back in our set K, the description of pairs (x,y) as </span>(x, x-5)
makes sure that each x, produces a specific y, for example in K we have:
(5, 0), and we cannot have (5, a value ≠0), because it would not fit the description (x, x-5)
Answer: yes
