Question

Which pair of points forms a line that does not intersect the line that passes through the points (5, 7) and (7, 7)?

Answer 1

Two lines which won't intersect are parallel, therefore you can pick a random y and add it to both points. This results in two new points forming a new line with the same slope.
So if you pick 1 you get the points (5,8),(7,8)
You may notice that the y coordinate is identical, so your slope is 0, parallel to the x axis and any two points with the same y $\neq$ 7 fulfill your question.