Definition of Asymptote[Calculus and Analytic Geometry, Thomas, Finney, 9E]
What is the asymptote of a straight line,y=mx+c?
My attempt
Every parallel line meets at infinity in the extended real line. Hence Every parallel line to the line $y=mx+c$ are asymptotes of $y=mx+c$. Therefore asymptotes are of the form $y=mx+d,d\in \mathbb R.$
Is there any error in my understanding?
The distance between two straight lines remains constant. The only straight line such that its distance from the graph of $y=mx+c$ approaches $0$ is the line $y=mx+c$ itself (in which case that distance is actually $0$ everywhere).