Final answer:
The question is about points on a line in Geometry, but the notation used for the points is unconventional and leads to ambiguities. Clarification on what 'a[3]' and 'b[-6]' represent is necessary to provide an accurate answer.
Step-by-step explanation:
The question pertains to points on a line in a coordinate system, which is a concept in Geometry, a branch of mathematics. However, there seems to be confusion or typographical issues in how the points are expressed: "let a[3] and b[-6] be two points on a line" traditionally doesn't align with the conventional notation for points in a coordinate plane.
Points are generally denoted as (x, y) coordinates. For instance, if we are to understand the points as a(3) and b(-6), they could represent the x-coordinates of two points along a line on a one-dimensional axis. Alternatively, if a and b are to denote different lines, then [3] and [-6] would not typically represent points on these lines.
To properly assist with the question, we would need clarification on what [3] and [-6] represent. Without this information, we cannot accurately discuss the properties of the line(s) mentioned or any related concepts such as the slope, distance between points, or equations representing the line(s).