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
