The slope of a horizontal line is 0. It only has a y-intercept.
y = mx + b
y = b, is a horizontal line (it only has a y-intercept "b")
In this case:
y = 7 is horizontal
y = 8 is horizontal
y = -1/7 is horizontal
All horizontal lines are parallel, so y = 8 and y = -1/7 are parallel to y = 7