This topic is covered in lesson G7a – Coordinates
When considering coordinates from an algebraic point of view, a key point to note is the following:
- You can specify points on a grid using coordinates. These are most commonly are of the form (x, y).
- You can specify straight lines (as well as many curves) on a grid using equations. These equations give you the relationship between the x and y coordinates of every point on the line.
For example, every point on the line y = x has an x coordinate which equals its y coordinate. Such points include (1, 1), (2, 2), (3, 3) etc. but also (1.7, 1.7)… There are infinitely many points on the line, but the equation perfectly defines the line.