The only linear equations that are not functions are equations
of vertical lines.  They have equations of the form x = a. 

such as x = 4 or x = -6 etc.

All other linear equations are functions.  A vertical line does
not pass the vertical line test.  That sounds funny, but it's true.

If you look at a vertical line, such as x=4



That illustrates two different points (4,3) and (4,-5) which gives
different outputs y=3 and y=-5 for the same input x=4.  In order to
represent a function, a graph cannot contain two different points
with the same x-value.

Another way of saying it is "In order for a graph to represent a
function, it must not contain any two points such that one is directly
above the other or directly below the other.  (4,3) is directly above
(4,-5) and (4,-5) is directly below (4,3).  So the graph cannot
represent a function.

Edwin