ElI5 What is the difference between the vector form of a line and the parametric form?

Question

ElI5 What is the difference between the vector form of a line and the parametric form?

In: 1

Answer 1

The vector form is still in the form y=f(x) = a*x + b, except a and b are multidimensional vectors. The parameterization is of the form y=f1(s), x=f2(s)

Edit: This was not simple enough, so let’s dig deeper.
Let’s think about what y=f(x) means.

Imagine a rollercoaster in 2D. It goes up and down, accelerates, and decelerates. The vector form is like the first-person POV, and the parameterization is the third-person POV