They are not.A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
All linear equations are functions but not all functions are linear equations.
There is one form of linear equation that is not a function, and that is when x = c, where c is a constant.
Some examples:f(x)= 3x + 2f(x)= xf(x)= -2x -1
Y=x