What is the difference between a straight line and a linear equation?

Question

The books I am reading do not make clear distinction between the two. Also for understanding line I need to know basics of Geometry, similarly what prior knowledge is useful before one can understand linear equations?

Answer 1

In the plane the two are pretty much the same concept. More strictly speaking, a linear equation is one way of characterizing the set of points which make up a given line. There are other ways, e.g. using starting point and direction vector.

In higher dimensions things change: a line will always be the geometric concept of a one-dimensional affine subspace, while a linear equation will describe a hyperplane, a subspace one dimension less than the containing space.

Answer 2

When there is a direct relation between $x,y$ we have $ y =m x. $ This is a straight line passing through the origin.This is direct proportional dependence.

In a relationship $ y=mx+c$ the graph does not pass through the origin. At start $x=0,$ there is already a constant value available.

Both are linear in their relationship between the two variables and their graphs are represented by a straight line.