Affine line in a vector space
= Affine line in a vector space
{title2=$a+kv=\{a+tv:t\in k\},\quad v\ne0$}
In a <vector space> over a <field> $k$, an affine line is a translate of a one-dimensional <vector subspace>. Its direction is that <vector subspace>, so multiplying $v$ by a nonzero scalar preserves the direction. Over a <finite field> of size $q$ it contains exactly $q$ distinct points. This usage concerns affine subsets of vector spaces, rather than the <affine line> as an <affine scheme>.