Final answer:
The set of possible coordinates for point a on a horizontal line passing through b(-4,-8) have the same y-coordinate as b, which is -8, and any real number as the x-coordinate.
Step-by-step explanation:
The set of possible coordinates of a point a which lies on a horizontal line passing through b(-4,-8) can be determined by understanding that all points on a horizontal line have the same y-coordinate.
Therefore, the y-coordinate of point a will be -8, similar to point b. The x-coordinate of point a can be any real number since the line extends infinitely in the horizontal direction.
To express this formally, the set of possible coordinates for point a is given by x ∈ ℝ, where ℝ is the set of all real numbers.