Can you give us an example of a linear equation that is not a function?

Maybe something like x=5, a vertical line.

Any equation that does not have a 'y' variable is not a function.
Ex. x = 3
x = 2
x = 84

A relation can be one many, i.e. for one input in domain, you get two values in range
or
A relation can be many one, i.e. for several inputs in domain, you get one value in range

rule of thumb!! A one many relation is not a function, but a many one relation is a function
example

y = x^2 is a function, for x = -a, +a you get one value of y
but x = y^2 is not a function, for x = a^2, y = +a, -a
or a better form to deduce it from graphs,
if a straight line parallel to x axis cuts the graph at more than one point, it is a function ( or at only one point)
if a straight line parallel to y axis cuts the graph at more than one point, it is not a function

so, any linear equation, is always a function