Parametric Equations :((

[David1717]

I have a line equation written in a form of (1 2 3 4)+t(5 6 7 8)
t is a proportionality factor
How I can get a line equation to check whether a point (a b c d) is on the line?

[jim360]

If (a b c d) is a point on the line r = (1 2 3 4) + (5 6 7 8)t then there will be some value of t that makes a = 1 +5t, b = 2+6t, c = 3 +7t, d = 4 + 8t, for the same t. So to check if a given point, say (6 8 10 12), is on the line, solve one of the equations a = 1 +5t so that t= (a-1)/5, and check that this t gives the other three values in the point.