Which point lies on the line defined by3x plus 6y equals 2?

Answer 1

Infinitely many points lies on this line (that's what a line is) but, not ALL points lie on this line.

Assuming it's not complex analysis (If you don't know of a phrase, you are not doing it, that's my moto).

Take the real plane with the usual x-axis and y-axis. The set of all points can be expressed as {(x, y) : 3x + 6y = 2, x, y are REAL} or any x and y satisfies 3x + 6y = 2 (there are many such points)

For simplicity, without loss of generality, we can fix an arbitrary x, and rearrange the equation so y = (2 - 3x)/6. So you can also write the set of points as {(x, (2 - 3x)/6 : x is real}

Similar, you can write it terms of y {((2 - 6y)/3, y) : y is real}